Observational Cosmology: An Introduction Wolfgang Hillebrandt MPI für Astrophysik Garching NOVICOSMO 2009 Rabac, Croatia September 20 - 30, 2009

Observational Cosmology:Observational Cosmology:An IntroductionAn Introduction

Wolfgang Hillebrandt MPI für Astrophysik

Garching

NOVICOSMO 2009 Rabac, Croatia

September 20 - 30, 2009

Acknowledgement:

To some extend, these lectures are based on a lecture series given by Matthias Steinmetz at the University of Arizona, Tucson.

The “new” Cosmos….The “new” Cosmos….

Outline of the lecturesOutline of the lectures

Historical overviewHistorical overview The “standard model” of cosmology The “standard model” of cosmology Classical tests and predictionsClassical tests and predictions

• The cosmic expansion rate The cosmic expansion rate

• (The cosmic microwave background )(The cosmic microwave background )

• Primordial nucleosynthesisPrimordial nucleosynthesis Formation of large-scale structure (and galaxies)Formation of large-scale structure (and galaxies)

Historical OverviewHistorical Overview

Aristotle (~350 B.C.): First Aristotle (~350 B.C.): First coherent physical modelcoherent physical model

Everything on Earth composed of four elements: Everything on Earth composed of four elements: earth, water, air and fireearth, water, air and fire

Each of these elements moves differently: earth toward Each of these elements moves differently: earth toward the center of the Universe, fire away from the center, the center of the Universe, fire away from the center, water and air occupy the space between.water and air occupy the space between.

Earth at the center of the UniverseEarth at the center of the Universe Objects of different composition fall differentlyObjects of different composition fall differently Concept of force: Motions that deviate from the natural Concept of force: Motions that deviate from the natural

motion of the element must be sustained by a force.motion of the element must be sustained by a force.

Aristotle’s cosmologyAristotle’s cosmology In contrast to Earthly motions, celestial motions In contrast to Earthly motions, celestial motions

continue indefinitely continue indefinitely two types of motion: two types of motion: limited, straight towards/away from the center limited, straight towards/away from the center (Earthly realm) (Earthly realm) and and continuing on circles in the continuing on circles in the heavensheavens

Celestial bodies cannot be composed of Celestial bodies cannot be composed of Earthly Earthly elementselements etherether as a fifth element as a fifth element

Limited motion on EarthLimited motion on Earth//indefinite motion in the indefinite motion in the heavensheavens reflect reflect imperfect Earthimperfect Earth//perfect heavensperfect heavens

Eternal and unchanging heavens Eternal and unchanging heavens Universe Universe without beginning or endwithout beginning or end

Universe has a finite sizeUniverse has a finite size

Aristarchus (~250 B.C.): the Sun Aristarchus (~250 B.C.): the Sun at the center at the center

He knew the size of the Earth (roughly)He knew the size of the Earth (roughly) He knew the size of the Moon and the distance between the He knew the size of the Moon and the distance between the

Moon and the Earth (from lunar eclipses)Moon and the Earth (from lunar eclipses) Using basic geometry, he was able to determine the size and Using basic geometry, he was able to determine the size and

distance of the Sundistance of the Sun Result: The Sun is 19 times Result: The Sun is 19 times [today’s value: 390 times] [today’s value: 390 times] more more

distant than the Moon and (because it has the same apparent distant than the Moon and (because it has the same apparent size on the sky) is 19 times larger than the Moon (and also size on the sky) is 19 times larger than the Moon (and also much larger than Earth)much larger than Earth)

Conclusion: the Sun (i.e. the largest object) is at the center of Conclusion: the Sun (i.e. the largest object) is at the center of the universethe universe

Aristarchus: Measuring the distance of the SunAristarchus: Measuring the distance of the Sun

Aristarchus: Why was his model never accepted Aristarchus: Why was his model never accepted

by his contemporaries?by his contemporaries?

He was considered a mathematician, not an He was considered a mathematician, not an astronomerastronomer

He stood against the two main authorities of his He stood against the two main authorities of his time, Aristotle and Hipparchustime, Aristotle and Hipparchus

His model was in conflict with the physics of His model was in conflict with the physics of his time, in particular Aristotle’s physicshis time, in particular Aristotle’s physics• no evidence for the Earth rotatingno evidence for the Earth rotating

• no evidence for the Earth movingno evidence for the Earth moving

Ptolemy (~100 A.D.): Ptolemy (~100 A.D.): defines the cosmology for defines the cosmology for the next 1500 yearsthe next 1500 years

Assembled the astronomical knowledge Assembled the astronomical knowledge (basically Aristotle’s cosmology and (basically Aristotle’s cosmology and Hipparchus’ observations) Hipparchus’ observations) Almagest (The Almagest (The Great System)Great System)

Expanded and improved the modelsExpanded and improved the models Patched up inconsistencies Patched up inconsistencies Epicycle theory Epicycle theory but at the expense of giving up simplicitybut at the expense of giving up simplicity

Retrograde motionRetrograde motion

Epicycle modelEpicycle model

Problems of Ptolemy’s modelProblems of Ptolemy’s model

Model couldn’t fit observationsModel couldn’t fit observations• put the Earth off centerput the Earth off center

• epicycles upon epicyclesepicycles upon epicycles

• total of more than 100 epicycles total of more than 100 epicycles

• Nevertheless errors in the predicted Nevertheless errors in the predicted positions of planets accumulated to positions of planets accumulated to several degrees by ~ 1400 A.D.several degrees by ~ 1400 A.D.

King Alfonso X (1221-1284): King Alfonso X (1221-1284): ““If the Lord Almighty had consulted me before If the Lord Almighty had consulted me before embarking upon Creation, I should have embarking upon Creation, I should have recommended something simplerrecommended something simpler””

The Copernican Revolution (~1500)The Copernican Revolution (~1500)

15th century: rediscovery of Greek scientific 15th century: rediscovery of Greek scientific thoughtthought

Shape and size of the Earth were well Shape and size of the Earth were well known among educated people (Columbus known among educated people (Columbus myth)myth)

Nicholas Copernicus Nicholas Copernicus De revolutionibus De revolutionibus orbium coelestrium orbium coelestrium [On the Revolution of [On the Revolution of Heavenly Spheres]: put the Sun at the center Heavenly Spheres]: put the Sun at the center heliocentric world model [inspired by the heliocentric world model [inspired by the work of Aristarchus ?]work of Aristarchus ?]

Why is the heliocentric model so Why is the heliocentric model so attractive ?attractive ?

It’s simpleIt’s simple It naturally explains why the inner It naturally explains why the inner

planets [Mercury and Venus] never travel far planets [Mercury and Venus] never travel far from the Sun from the Sun

Reproduces much better the observed change Reproduces much better the observed change in brightness of planetsin brightness of planets

It provides a natural explanation for the It provides a natural explanation for the seasonsseasons

It provides a natural explanation of retrograde It provides a natural explanation of retrograde motions without relying on epicyclesmotions without relying on epicycles

Heliocentric modelHeliocentric model

Problems of the heliocentric model Problems of the heliocentric model (at that time)(at that time)

Against Christian ScripturesAgainst Christian Scriptures New discoveryNew discovery Predicts parallaxes Predicts parallaxes observationobservation Problem rotating Earth Problem rotating Earth Aristotle’s physicsAristotle’s physics Less accurate than the Ptolemaic model Less accurate than the Ptolemaic model

working model required even more epicyclesworking model required even more epicycles Question: Question: Why did he published his work only Why did he published his work only

near the end of his life ? Was he afraid of the near the end of his life ? Was he afraid of the authority of the Church, or was he embarrassed authority of the Church, or was he embarrassed because of the “failure” of his model ?because of the “failure” of his model ?

Just being smart is not enough ...Just being smart is not enough ...

Better dataBetter data

Final touch-up of the Final touch-up of the modelmodel

Promotion of the Promotion of the new modelnew model

Tycho BraheTycho Brahe

Johannes KeplerJohannes Kepler

Galileo GalileiGalileo Galilei

Tycho Brahe (1546-1601)Tycho Brahe (1546-1601) Last of the great naked-eye observersLast of the great naked-eye observers exceptionally careful and systematic exceptionally careful and systematic

observer observer first modern scientist first modern scientist Earth at center, planets orbit the SunEarth at center, planets orbit the Sun detailed measurement of Mars’ orbit over 30 yearsdetailed measurement of Mars’ orbit over 30 years Observed comets and parallax of comets Observed comets and parallax of comets Comet Comet

behind the orbit of the Moonbehind the orbit of the Moon Observed a supernova [“new star”] in Cassiopeia, Observed a supernova [“new star”] in Cassiopeia,

no parallax measurable no parallax measurable supernova must be on supernova must be on celestial sphere celestial sphere

Challenge of the Aristotelian idea of the perfect, Challenge of the Aristotelian idea of the perfect, eternal, unchanging heavens eternal, unchanging heavens

Johannes Kepler (1571-1630)Johannes Kepler (1571-1630)

Tycho’s successor in PragueTycho’s successor in Prague He realized that neither the Ptolemaic He realized that neither the Ptolemaic

nor Tycho’s nor the heliocentric model nor Tycho’s nor the heliocentric model can fit Tycho’s data within the stated accuracycan fit Tycho’s data within the stated accuracy

Proposal: planets move on ellipses, not circlesProposal: planets move on ellipses, not circles

Galileo Galilei (1564-1642)Galileo Galilei (1564-1642)

Has not invented the telescope !Has not invented the telescope ! But: was the first to point the But: was the first to point the

telescope at the night skytelescope at the night sky Designed tests for Aristotle’s physics and Designed tests for Aristotle’s physics and

finally rejected itfinally rejected it Famous for his trial for heresy 1633Famous for his trial for heresy 1633 Exonerated only in 1979 !Exonerated only in 1979 !

Galileo’s astronomical discoveriesGalileo’s astronomical discoveries

Mountains on the Moon similar to EarthMountains on the Moon similar to Earth not perfect spherical bodies not perfect spherical bodies

Stars: point like; planets: spheresStars: point like; planets: spheres Phases of Venus Phases of Venus Ptolemaic world systemPtolemaic world system Moons of Jupiter Moons of Jupiter miniature system miniature system Interpretation of Sun spots Interpretation of Sun spots unchangingunchanging

heavensheavens Milky Way = Zillions of StarsMilky Way = Zillions of Stars

Galileo’s physicsGalileo’s physics

Concept of inertia and momentum:Concept of inertia and momentum:

• Aristotle: force is responsible for motionAristotle: force is responsible for motion

• Galileo: force is responsible forGalileo: force is responsible for changeschanges in in motionmotion

relativity of uniform motionrelativity of uniform motion Fall experiments: objects of different composition Fall experiments: objects of different composition

fall at the same rate fall at the same rate AristotleAristotle basis for Einstein’s equivalence principle basis for Einstein’s equivalence principle

Thought experimentsThought experiments

Better dataBetter data

Final touch-up of Final touch-up of the modelthe model

Promotion of the Promotion of the new modelnew model

Tycho BraheTycho Brahe

Johannes KeplerJohannes Kepler

Galileo GalileiGalileo Galilei

Still missing: Still missing: someone to put the pieces someone to put the pieces together to form a coherent physical theory together to form a coherent physical theory in the modern sense in the modern sense Sir Isaac NewtonSir Isaac Newton

Sir Isaac Newton Sir Isaac Newton (1643-1727)(1643-1727)

Fundamental contributions in Fundamental contributions in optics, physics and mathematics:optics, physics and mathematics:

• invented calculus (independently: Leibnitz)invented calculus (independently: Leibnitz)

• invented the mirror telescopeinvented the mirror telescope

• discovered that white light is composed of colored discovered that white light is composed of colored lightlight

• theory of mechanicstheory of mechanics

• theory of gravitytheory of gravity

• demonstrated that Kepler’s laws are a consequence of demonstrated that Kepler’s laws are a consequence of the theory of mechanics and gravity: the theory of mechanics and gravity: PrincipiaPrincipia

Newton’s triumph: discovery of NeptuneNewton’s triumph: discovery of Neptune

1781: W. Herschel discovers Uranus1781: W. Herschel discovers Uranus Measurements of Uranus’ orbit around the Sun: Measurements of Uranus’ orbit around the Sun:

slight deviations from perfect ellipse. These slight deviations from perfect ellipse. These cannot be accounted for by the perturbing cannot be accounted for by the perturbing influence of the known planets influence of the known planets another planet ?another planet ?

Leverrier and Adams calculated the position of a Leverrier and Adams calculated the position of a hypothetical planet that could be responsible for hypothetical planet that could be responsible for the observed deviationsthe observed deviations

Galle (1846) pointed a telescope to the predicted Galle (1846) pointed a telescope to the predicted position and found the new planet (Neptune) position and found the new planet (Neptune) within 1° of the predicted positionwithin 1° of the predicted position

Next step: apply Newton’s laws to cosmologyNext step: apply Newton’s laws to cosmology

Problem: ~1750 “universe” identical with solar Problem: ~1750 “universe” identical with solar system. Stars far away, but how far ?system. Stars far away, but how far ?

We need empirical data regarding the size and We need empirical data regarding the size and age of the universe, so we can compare model age of the universe, so we can compare model predictions against datapredictions against data

Determining the Size and Determining the Size and Age of the UniverseAge of the Universe

??????

How do we measure distances in “daily life” ?How do we measure distances in “daily life” ?

ParallaxesParallaxes Travel timeTravel time Via size of objects: comparison with standard Via size of objects: comparison with standard

yard sticksyard sticks Via brightness of objects: comparison with Via brightness of objects: comparison with

standard candlesstandard candles

ParallaxesParallaxes Measure the position of an object with respect to its Measure the position of an object with respect to its

backgroundbackground Nearby objects show a larger “motion” than objects far Nearby objects show a larger “motion” than objects far

away doaway do The parallax angle The parallax angle , the distance of the object , the distance of the object D D and and

the diameter of the Earth’s orbitthe diameter of the Earth’s orbit d d are connected by are connected by simple geometrical relations. For small angles, it issimple geometrical relations. For small angles, it is

d = D d = D [units !!!! [units !!!! measured in rad ! measured in rad !]]

Travel timeTravel time

If you know the speed If you know the speed vv you’re traveling with and you’re traveling with and the travel time the travel time tt, the distance , the distance DD can be obtained can be obtained by simple multiplication: by simple multiplication: D = v D = v tt

Astronomy:Astronomy: Use light travel times Use light travel times, , i.e. i.e. vv = 300 000 km/sec = 300 000 km/sec

Comparison with a standard rulerComparison with a standard ruler

An object nearby spans a larger angle than an An object nearby spans a larger angle than an object of identical physical size far awayobject of identical physical size far away

The physical size The physical size ll of the object, its distance of the object, its distance DD and and the angle the angle qq under which it appears are connected under which it appears are connected by simple geometrical relations. For small angles, by simple geometrical relations. For small angles, it isit is l = D l = D q q [[units !!!! units !!!! qq measured in rad !measured in rad !]]

If the physical size If the physical size ll of an object is known (of an object is known ( standard rulerstandard ruler), its distance ), its distance DD can be determined can be determined by measuring the angle by measuring the angle qq under which the object under which the object appearsappears

Comparison with a standard candleComparison with a standard candle

A nearby object appears brighter than an object of A nearby object appears brighter than an object of same luminosity far awaysame luminosity far away

The absolute luminosity The absolute luminosity LLabsoluteabsolute of an object, its of an object, its distance distance DD and its apparent luminosity and its apparent luminosity LLapparentapparent are are connected by simple geometrical relations. It isconnected by simple geometrical relations. It is LLapparent apparent = L= L

absoluteabsolute / D / D22 If the If the absolute luminosity absolute luminosity LLabsoluteabsolute of an object is of an object is

known (known ( standard candle standard candle), its distance ), its distance DD can be can be determined by measuring its apparent luminositydetermined by measuring its apparent luminosity LLapparentapparent

Three Types of Distance MeasurementThree Types of Distance Measurement

Direct Measurements:Direct Measurements: Measuring the physical Measuring the physical

distance to an object directlydistance to an object directly

Standard Rulers: Standard Rulers: Size = Distance x q(angle on sky)Size = Distance x q(angle on sky)

Need to know the real size of the object Need to know the real size of the object

Standard Candles: Standard Candles: LLapparent apparent = L= Labsoluteabsolute / D / D22

Need to know the true luminosity of an objectNeed to know the true luminosity of an object

Direct MeasurementsDirect Measurements (Important!)(Important!)

Light Travel Time:Light Travel Time: Measure the time taken for a radar pulse to bounce Measure the time taken for a radar pulse to bounce

off of an object or a signal to arrive from a off of an object or a signal to arrive from a spacecraft: solar systemspacecraft: solar system

Parallax:Parallax: good to ~1 kpc (astrometry from space!)good to ~1 kpc (astrometry from space!)

Standard RulersStandard Rulers

Expanding Photosphere Method (EPS or Expanding Photosphere Method (EPS or Baade-Wesselink)Baade-Wesselink)• Type II supernova explosionsType II supernova explosions

• Measure speed of expansion of debris and Measure speed of expansion of debris and time since explosion time since explosion real size of nebula real size of nebula

• Useful to distances of 10-100 MpcUseful to distances of 10-100 Mpc

(Most recent paper: Jones et al., ApJ (Most recent paper: Jones et al., ApJ 696696 (2009) 1176) (2009) 1176)

Standard Rulers Standard Rulers

Water Masers: Water Masers: Measure the proper motions and accelerations of Measure the proper motions and accelerations of

water masers in the accretion disks of AGN to get water masers in the accretion disks of AGN to get actual orbital radius of masers and mass of central actual orbital radius of masers and mass of central object. Only very few measurements so far.object. Only very few measurements so far.

(Strong) Gravitational lensing: (Strong) Gravitational lensing: Time delay of fluctuations in lensed object gives Time delay of fluctuations in lensed object gives

info on geometry. Depends on mass of lens and info on geometry. Depends on mass of lens and theoretical lensing model. Good to ~ 1 Gpctheoretical lensing model. Good to ~ 1 Gpc

Standard Rulers (Important!) Standard Rulers (Important!)

Baryon acoustic oscillations (BAO): Baryon acoustic oscillations (BAO): Arise from the competition between gravitational Arise from the competition between gravitational

attraction and gas pressure in the primordial plasma. attraction and gas pressure in the primordial plasma. Imprint on scales ~ 100Mpc/h.Imprint on scales ~ 100Mpc/h.

Weak lensing: Weak lensing: Images of source galaxies can be stretched (shear) and Images of source galaxies can be stretched (shear) and

magnified (convergence). Relies on statistics of the magnified (convergence). Relies on statistics of the lensed population. lensed population.

CMB:CMB: Horizon size at the time of hydrogen recombination.Horizon size at the time of hydrogen recombination.

Standard Candles Standard Candles Main Sequence fitting: Calibrate the luminosity of Main Sequence fitting: Calibrate the luminosity of

main sequence stars in nearby clusters with parallax main sequence stars in nearby clusters with parallax distances and fit clusters farther out. Good to 10-100 distances and fit clusters farther out. Good to 10-100 kpc.kpc.

Standard Candles (Important!)Standard Candles (Important!)

Cepheid and RR Lyrae variablesCepheid and RR Lyrae variables• Pulsating stars which change in brightness with a Pulsating stars which change in brightness with a

characteristic periodcharacteristic period• Period is proportional to absolute luminosityPeriod is proportional to absolute luminosity• Common and bright (esp. Cepheids), thus visible Common and bright (esp. Cepheids), thus visible

in nearby galaxiesin nearby galaxies• Good to ~20 MpcGood to ~20 Mpc

Standard Candles (Important!)Standard Candles (Important!)

Surface brightness fluctuationsSurface brightness fluctuations Distant objects appear smallerDistant objects appear smaller More stars per pixel in a galaxy far, far awayMore stars per pixel in a galaxy far, far away Smoother light distribution, less variation Smoother light distribution, less variation

from pixel to pixelfrom pixel to pixel Amplitude of fluctuations proportional to Amplitude of fluctuations proportional to

distancedistance Good to ~100 Mpc, z~0.01Good to ~100 Mpc, z~0.01

Courtesy John Tonry

Standard Candles Standard Candles

Luminosity functionsLuminosity functions Choose a type of object with a charcteristic Choose a type of object with a charcteristic

distribution of absolute luminositiesdistribution of absolute luminosities Measure distribution of apparent luminosities in a Measure distribution of apparent luminosities in a

distant galaxydistant galaxy Scale to match true luminosities, get distanceScale to match true luminosities, get distance Globular clusters and planetary nebulae good to Globular clusters and planetary nebulae good to

~50-100 Mpc~50-100 Mpc

Standard Candles (Important!) Standard Candles (Important!)

Galaxy kinematicsGalaxy kinematics• Tully-Fisher relation: rotation speed of spiral Tully-Fisher relation: rotation speed of spiral

galaxies proportional to mass of glaxy galaxies proportional to mass of glaxy proportional to total luminosityproportional to total luminosity

• DDnn--σσ, “Fundamental Plane”, Faber-Jackson , “Fundamental Plane”, Faber-Jackson

relations: velocity dispersion and size of elliptical relations: velocity dispersion and size of elliptical galaxies proportional to total luminositygalaxies proportional to total luminosity

• Good to ~500 Mpc, z~0.1Good to ~500 Mpc, z~0.1

Standard Candles (Important!) Standard Candles (Important!)

Type Ia supernovaeType Ia supernovae• Exploding white dwarf starExploding white dwarf star• Shape of light curve and dimming timescale give Shape of light curve and dimming timescale give

absolute luminosityabsolute luminosity• Extermely luminous so they can be observed at Extermely luminous so they can be observed at

great distancesgreat distances• Good to ~1 Gpc, z~1Good to ~1 Gpc, z~1

The Distance LadderThe Distance Ladder

Different techniques useful at different Different techniques useful at different distances: use nearby standards to calibrate more distances: use nearby standards to calibrate more distant ones where they overlapdistant ones where they overlap

Cepheids are a key step:Cepheids are a key step: many in the Milky Way many in the Milky Way and LMC, so distances are directly measurable and LMC, so distances are directly measurable by parallax or only a step away, yet bright by parallax or only a step away, yet bright enough to overlap many secondary distance enough to overlap many secondary distance indicatorsindicators

Cepheids Cepheids luminosity functions, SBF, galaxy luminosity functions, SBF, galaxy kinematics, SNIa, SZ, BAO, WL, CMBkinematics, SNIa, SZ, BAO, WL, CMB

Size of the Universe (I)Size of the Universe (I)

Size of the Earth:Size of the Earth:• radius 6370 kmradius 6370 km

• Eratosthenes (~200 B.C.)Eratosthenes (~200 B.C.) Size of the solar systemSize of the solar system

• several billion kmseveral billion km

• rough idea: Aristarchus (~250 B.C.)rough idea: Aristarchus (~250 B.C.)

• detailed layout: ~1750detailed layout: ~1750

Size of the Universe (II)Size of the Universe (II)

Distance to the starsDistance to the stars• until 1838: far awayuntil 1838: far away

• Bessel (1838): measured the first parallax of a star Bessel (1838): measured the first parallax of a star (61 Cygni). Result: 0.3”(61 Cygni). Result: 0.3”

• So how far is 61 Cygni ? Recall:So how far is 61 Cygni ? Recall:

d = D d = D

D = 149.7 D = 149.7 10106 6 km/1.45 km/1.45 1010--

66 10 101414 km km 10Ly 10Ly

Shape and Size of the Milky WayShape and Size of the Milky Way

~1600 Galileo: MW = collection of stars~1600 Galileo: MW = collection of stars ~1750 Immanuel Kant, Thomas Wright:~1750 Immanuel Kant, Thomas Wright:

MW is a diskMW is a disk ~1780 Herschel: counted stars in ~700 fields ~1780 Herschel: counted stars in ~700 fields

around the sky: MW is flattened 4:1, Sun is around the sky: MW is flattened 4:1, Sun is near the centernear the centerbut is it ?but is it ?

Size of the Milky WaySize of the Milky Way

Kapteyn (~1920)Kapteyn (~1920) measures distances to measures distances to

stars in the MWstars in the MW conclusion:conclusion:

• MW about 5 kpc acrossMW about 5 kpc across

• Sun near the centerSun near the center

Shapley (~1920)Shapley (~1920) measured distances to measured distances to

globular clustersglobular clusters conclusion:conclusion:

• MW about 100 kpc MW about 100 kpc acrossacross

• Sun 20 kpc off centerSun 20 kpc off center

Solution ???Solution ???

Nature of spiral nebulae ?Nature of spiral nebulae ?

CurtisCurtis MW is 10 kpc acrossMW is 10 kpc across Sun near centerSun near center spiral nebulae were other spiral nebulae were other

galaxiesgalaxies• high recession speedhigh recession speed

• apparent sizes of nebulaeapparent sizes of nebulae

• did not believe van did not believe van Maanen’s measurementMaanen’s measurement

Milky Way = one galaxy Milky Way = one galaxy among many othersamong many others

ShapleyShapley MW is 100 kpc acrossMW is 100 kpc across Sun off centerSun off center spiral nebulae part of the spiral nebulae part of the

GalaxyGalaxy• apparent brightness of nova apparent brightness of nova

in the Andromeda galaxyin the Andromeda galaxy

• measured rotation of measured rotation of spirals (via proper motion) spirals (via proper motion) by van Maanenby van Maanen

Milky Way = UniverseMilky Way = Universe

Solution ISolution I

Role of dustRole of dust• obscuration: obscuration: Kapteyn/Curtis could only see a small Kapteyn/Curtis could only see a small

fraction of the Milky Way diskfraction of the Milky Way disk

• dimming:dimming: stars appear to be dimmer stars appear to be dimmer Shapley, Shapley, ignoring dust, concluded that globular clusters are ignoring dust, concluded that globular clusters are farther away than they actually are.farther away than they actually are.

Milky Way is 30 kpc across, Sun is 8.5 kpc off Milky Way is 30 kpc across, Sun is 8.5 kpc off center. center.

Solution IISolution II

Van Maanen’s observation (rotation of spiral Van Maanen’s observation (rotation of spiral nebulae) turned out to be wrong.nebulae) turned out to be wrong.

There is a difference between novae and There is a difference between novae and supernovae, supernovae are much brightersupernovae, supernovae are much brighter Andromeda is farther away than anticipated Andromeda is farther away than anticipated by Shapleyby Shapley

Spiral nebulae are galaxies like the Milky Spiral nebulae are galaxies like the Milky Way. Distance: millions of parsec.Way. Distance: millions of parsec.

Limits on the Age of the Universe (I): Limits on the Age of the Universe (I): Age of the Earth Age of the Earth

Before ~1670:Before ~1670: little attention, but common little attention, but common perception that the Earth is youngperception that the Earth is young

1669:1669: Nicolaus Steno: older rocks below, younger Nicolaus Steno: older rocks below, younger rocks above. Layering of rocks rocks above. Layering of rocks age sequence age sequence

~1800:~1800: Realization that Earth may be very old Realization that Earth may be very old 1858:1858: Wallace and Darwin: Evolution of species Wallace and Darwin: Evolution of species

Earth must be very old (hundreds of millions of Earth must be very old (hundreds of millions of years)years)

Limits on the Age of the Universe (II): Limits on the Age of the Universe (II): Age of the Earth/Sun Age of the Earth/Sun

Problem: Problem: in the 19th century, the Sun was in the 19th century, the Sun was believed to be only 100 million years old (it believed to be only 100 million years old (it would run out of fuel otherwise)would run out of fuel otherwise)

Solution:Solution: nuclear fusion (Eddington-Bethe-nuclear fusion (Eddington-Bethe-Weizsäcker 1930s)Weizsäcker 1930s)

Today:Today: radioactive dating of rocks radioactive dating of rocks Earth (and Earth (and solar system) is 4.6 billion years oldsolar system) is 4.6 billion years old

Later in these lectures:Later in these lectures: age of the universe ~ 14 age of the universe ~ 14 billion yearsbillion years

Let’s come back to Newton’s UniverseLet’s come back to Newton’s Universe

In order to avoid collapseIn order to avoid collapse homogeneoushomogeneous isotropicisotropic infinite sizeinfinite size no centerno center

Infinite in timeInfinite in time has always beenhas always been will always bewill always be

(perfect) cosmological principle!(perfect) cosmological principle!

The cosmological principleThe cosmological principle

Homogeneous: Homogeneous: the universe looks the same the universe looks the same everywhere on large scaleseverywhere on large scales there is no special place (center) there is no special place (center)

Isotropic:Isotropic: the universe looks the same in all the universe looks the same in all directions on the skydirections on the sky

there is no special direction (axis)there is no special direction (axis)

Homogeneity and IsotropyHomogeneity and Isotropy

IsotropyIsotropyCopernicanCopernican

PrinciplePrincipleHomogeneityHomogeneity++

IsotropyIsotropy Isotropy around Isotropy around another pointanother point HomogeneityHomogeneity++

Does the cosmological principle apply to our Does the cosmological principle apply to our universe ?universe ?

The cosmic microwave The cosmic microwave

background radiation (CMB)background radiation (CMB)

= afterglow from the big bang.= afterglow from the big bang.

It’s smooth to 1 part in 10It’s smooth to 1 part in 1055

Yes, the universe appears Yes, the universe appears to be homogeneous to be homogeneous and isotropic! and isotropic!

Each shell contributesEach shell contributes

LL11 = 4 = 4 r r1122x lx l**

infinite number of shellsinfinite number of shells

infinite luminosityinfinite luminosity

Problems with an infinite universeProblems with an infinite universe

Olber’s Paradox: Why is the night sky dark?Olber’s Paradox: Why is the night sky dark?

How to solve Olber’s paradox ?How to solve Olber’s paradox ?

Universe is finiteUniverse is finite Universe has finite ageUniverse has finite age The distribution of stars throughout space is The distribution of stars throughout space is

not uniformnot uniform The wavelength of radiation increases with The wavelength of radiation increases with

time. time.

Note:Note: for the big bang model, all thesefor the big bang model, all these conditions are satisfied conditions are satisfied

Two clouds on the horizon of Two clouds on the horizon of 19th century physics19th century physics

Michelson-Morley resultMichelson-Morley result Thermal radiation of hot bodies (so-called Thermal radiation of hot bodies (so-called

black body radiation)black body radiation)

Two hurricanes resultTwo hurricanes result

Theory of relativityTheory of relativity Quantum mechanicsQuantum mechanics

Einstein’s new relativityEinstein’s new relativity

Galileo:Galileo:

• The The laws of mechanicslaws of mechanics are the same in all are the same in all inertial frames of referenceinertial frames of reference

• time and spacetime and space are the same in all inertial frames are the same in all inertial frames of referenceof reference

Einstein:Einstein:

• The The laws of physicslaws of physics are the same in all inertial are the same in all inertial frames of referenceframes of reference

• thethe speed of light in the vacuum speed of light in the vacuum is the same in is the same in all inertial frames of referenceall inertial frames of reference

time spans and distances are relativetime spans and distances are relative

Doppler effectDoppler effect

redshift:redshift:

zz=0: not moving=0: not moving

zz=2: =2: vv=0.8=0.8cc

zz==: : vv==cc

cv

cvz

/1

/11

cv

cvz

/1

/11

Some open problems of special relativitySome open problems of special relativity

How to deal with accelerations ?How to deal with accelerations ? How to deal with gravity ?How to deal with gravity ? Newton’s gravity acts instantaneously, i.e. it Newton’s gravity acts instantaneously, i.e. it

is inconsistent with special relativity’s is inconsistent with special relativity’s conclusion that information cannot be conclusion that information cannot be communicated faster than the speed of light.communicated faster than the speed of light.

Distance is relative, so which distance to use Distance is relative, so which distance to use in computing the gravitational force ?in computing the gravitational force ?

General relativityGeneral relativity

Mass tells space how to curveMass tells space how to curve

Space tells mass how to moveSpace tells mass how to move

The entire Universe in one lineThe entire Universe in one line

T

c

GG

4

8

Tc

GG

4

8

Geometry of Geometry of

spacetimespacetime

(Einstein tensor)(Einstein tensor)

Distribution ofDistribution of

mass and energymass and energy

in the universein the universe

(stress-energy tensor)(stress-energy tensor)

Some effects predicted by the theory of Some effects predicted by the theory of general relativitygeneral relativity

Gravity bends lightGravity bends light Gravitational redshiftGravitational redshift Gravitational time dilationGravitational time dilation Gravitational length contractionGravitational length contraction

Examples for light bendingExamples for light bending


“Einstein Cross” - G2237+0305



How to find out that space is not flat?How to find out that space is not flat?

How to find out that space is not flat?How to find out that space is not flat?

In flat spaceIn flat space

++ = 180º

In curved spaceIn curved space

++ 180º

Newton’s LawsNewton’s Laws

Newton’s Law Newton’s Law of Gravityof Gravity

History of CosmologyHistory of Cosmology

Special RelativitySpecial Relativity

General RelativityGeneral Relativity

Cosmic Distance Cosmic Distance LadderLadder

Size and Age Size and Age of the Universeof the Universe ????

Break!Break!

The Scientific MethodThe Scientific Method

specific instancesspecific instances

observationsobservations

inductioninduction

general principlegeneral principle

deductiondeduction

predictionprediction

individual eventsindividual events

revisionrevision

Science is a history of corrected mistakes (Popper)Science is a history of corrected mistakes (Popper)

Karl Popper also:Karl Popper also:

“Good tests kill flawed theories; we remain “Good tests kill flawed theories; we remain alive to guess again.”alive to guess again.”

The “Standard Model” of The “Standard Model” of CosmologyCosmology

The entire Universe in one lineThe entire Universe in one line

T

c

GG

4

8

Tc

GG

4

8

Geometry of Geometry of

spacetimespacetime

(Einstein tensor)(Einstein tensor)

Distribution ofDistribution of

mass and energymass and energy

in the universein the universe

(stress-energy tensor)(stress-energy tensor)

Let’s apply Einstein’s equation to the UniverseLet’s apply Einstein’s equation to the Universe

What is the solution of Einstein’s equation for a What is the solution of Einstein’s equation for a homogeneous, isotropic mass distribution?homogeneous, isotropic mass distribution?• As in Newtonian dynamics, gravity is always As in Newtonian dynamics, gravity is always

attractiveattractive

• A homogeneous, isotropic and initially static A homogeneous, isotropic and initially static universe is going to collapse under its own gravityuniverse is going to collapse under its own gravity

• Alternative: expanding universe (Friedmann) Alternative: expanding universe (Friedmann)

Einstein’s proposal: cosmological constant Einstein’s proposal: cosmological constant

There is a repulsive force in the universeThere is a repulsive force in the universe vacuum exerts a pressurevacuum exerts a pressure empty space is curved rather than flatempty space is curved rather than flat

The repulsive force compensates the attractive The repulsive force compensates the attractive gravity gravity static universe is possible static universe is possible

but:but: such a universe turns out to be unstable: one such a universe turns out to be unstable: one can set up a static universe, but it simply does not can set up a static universe, but it simply does not remain staticremain static

Einstein: “greatest blunder of his life”, Einstein: “greatest blunder of his life”, butbut is it is it really … ? really … ?

The quantum vacuum acts like a gas of negative The quantum vacuum acts like a gas of negative pressure!pressure!

Edwin Hubble Edwin Hubble (1889-1953)(1889-1953)

Four major accomplishments Four major accomplishments in extragalactic astronomy:in extragalactic astronomy: The establishment of the The establishment of the

Hubble classification Hubble classification scheme of galaxiesscheme of galaxies

The convincing proof that galaxies are island The convincing proof that galaxies are island “universes”“universes”

The distribution of galaxies in spaceThe distribution of galaxies in space The discovery that the universe is expandingThe discovery that the universe is expanding

Again: the Doppler effectAgain: the Doppler effect

redshift:redshift:

zz=0: not moving=0: not moving

zz=2: =2: vv=0.8=0.8cc

zz==: : vv==cc

cv

cvz

/1

/11

cv

cvz

/1

/11

The redshift-distance relationThe redshift-distance relation

A “modern” Hubble diagramA “modern” Hubble diagram

Key resultsKey results

Most galaxies are moving away from usMost galaxies are moving away from us The recession speed v is larger for more distant The recession speed v is larger for more distant

galaxies. The relation between recess velocity galaxies. The relation between recess velocity vv and distance and distance dd fulfills a linear relation: fulfills a linear relation: v = Hv = H0 0 d d

Hubble’s measurement of the constant Hubble’s measurement of the constant HH00::

HH00 = 500 km/s/Mpc = 500 km/s/Mpc Today’s best fit value of the constant:Today’s best fit value of the constant:

HH00 = 72 km/s/Mpc = 72 km/s/Mpc

So why was Hubble’s original measurement So why was Hubble’s original measurement so far off ?so far off ?

Distance measurement based on the period-Distance measurement based on the period-luminosity relation of Cepheid starsluminosity relation of Cepheid stars

What are Cepheids? They are variable What are Cepheids? They are variable pulsating starspulsating stars


There exists a luminosity-period relation for There exists a luminosity-period relation for Cepheid starsCepheid stars


there are two populations of Cepheids (but there are two populations of Cepheids (but Hubble was not aware of that)Hubble was not aware of that)• type I: metal rich stars (disk of galaxies)type I: metal rich stars (disk of galaxies)

• type II: metal poor stars (halo of galaxies)type II: metal poor stars (halo of galaxies)

• type II Cepheids (“W Virginistype II Cepheids (“W Virginis”) ”) are less luminous are less luminous than type I Cepheids (“than type I Cepheids (“δδ Cephei” Cephei”))

ConsequenceConsequence

Distance scale was calibrated based on type II Distance scale was calibrated based on type II CepheidsCepheids

Distances to other galaxies were measured Distances to other galaxies were measured using type I Cepheids using type I Cepheids

““yard stick” was systematically too smallyard stick” was systematically too small

HH00 too large! too large!

How old is the universe ? (III)How old is the universe ? (III)

A galaxy at distance A galaxy at distance dd recedes at velocity recedes at velocity v=Hv=H0 0 d d.. When was the position of this galaxy identical to When was the position of this galaxy identical to

that of our galaxy? Answer: that of our galaxy? Answer:

0

1

Hv

dtHubble

0

1

Hv

dtHubble

ttHubbleHubble: Hubble time. : Hubble time.

For For HH00 = 72 km/s/Mpc: = 72 km/s/Mpc: ttHubbleHubble ≈≈14 Gyr14 Gyr

How big is the universe? (III)How big is the universe? (III)

We can’t tell. We can only see (and are affected by) We can’t tell. We can only see (and are affected by) that part of the universe that is closer than the that part of the universe that is closer than the distance that light can travel in a time distance that light can travel in a time corresponding to the age of the Universecorresponding to the age of the Universe

But we can estimate, how big the observable But we can estimate, how big the observable universe is:universe is:

0H

cctd HubbleHubble

0H

cctd HubbleHubble

ddHubbleHubble: Hubble radius. : Hubble radius.

For For HH00 = 72 km/s/Mpc: = 72 km/s/Mpc: ddHubbleHubble = 4.2 Gpc= 4.2 Gpc

The great synthesis (1930)The great synthesis (1930)

Meeting by Einstein, Hubble and LemaîtreMeeting by Einstein, Hubble and Lemaître• Einstein: theory of general relativityEinstein: theory of general relativity

• Friedmann and Lemaître: expanding universe as Friedmann and Lemaître: expanding universe as a solution to Einstein’s equationa solution to Einstein’s equation

• Hubble: observational evidence that the Hubble: observational evidence that the universe is indeed expandinguniverse is indeed expanding

Consequence:Consequence:• Universe started from a pointUniverse started from a point

The Big Bang Model ! The Big Bang Model !

A metric of an expanding UniverseA metric of an expanding Universe

Recall: flat spaceRecall: flat space

better: using spherical coordinates (better: using spherical coordinates (r,,))

22222 zyxtcs 22222 zyxtcs

)sin( 22222222 rrrtcs )sin( 22222222 rrrtcs


But, this was for a static (flat) space. How does But, this was for a static (flat) space. How does this expression change if we consider an this expression change if we consider an expanding space ?expanding space ?

a(t)a(t) is the so-called is the so-called scale factorscale factor

222222222 sin)( rrrtatcs 222222222 sin)( rrrtatcs


Robertson-Walker metricRobertson-Walker metric

a(t)a(t) is the is the scale factorscale factor k k is the curvature constantis the curvature constant

• k=0k=0: : flat spaceflat space

• k>0k>0: : spherical geometryspherical geometry

• k<0k<0: : hyperbolic geometryhyperbolic geometry

222222

2222 sin

1)( rr

kr

rtatcs

222222

2222 sin

1)( rr

kr

rtatcs


But, so far, we only considered a flat space. But, so far, we only considered a flat space. What, if there is curvature ?What, if there is curvature ?

k k is the curvature constantis the curvature constant• k=0k=0: flat space: flat space

• k>0k>0: spherical geometry: spherical geometry

• k<0k<0: hyperbolic geometry: hyperbolic geometry

k>0k>0 k<0k<0k=0k=0

Cosmological redshiftCosmological redshift

While a photon travels from a distance source While a photon travels from a distance source to an observer on Earth, the Universe expands to an observer on Earth, the Universe expands in size from in size from aathenthen to to aanownow..

Not only the Universe itself expands, but also Not only the Universe itself expands, but also the wavelength of the photon the wavelength of the photon ..

emittedthen

nowreceived a

a emittedthen

nowreceived a

a


General definition of redshift:General definition of redshift:

for cosmological redshift: for cosmological redshift:

emitted

emittedreceivedz

emitted

emittedreceivedz

then

now

emitted

received

a

az

1then

now

emitted

received

a

az

1


Examples:Examples:• z=1 z=1 aathenthen//aanownow = 0.5 = 0.5

at at z=1z=1, the universe had , the universe had 50% of its present day size50% of its present day size emitted emitted blue light blue light (400 nm) is shifted all the way (400 nm) is shifted all the way

through the optical spectrum and is received as through the optical spectrum and is received as red red light light (800 nm)(800 nm)

• z=4 z=4 aathenthen//aanownow = 0.2 = 0.2 at at z=4z=4, the universe had , the universe had 20% of its present day size20% of its present day size emitted emitted blue light blue light (400 nm) is shifted deep into the (400 nm) is shifted deep into the

infraredinfrared and is received at 2000 nm and is received at 2000 nm

• most distant astrophysical objects discovered so most distant astrophysical objects discovered so far: quasars at (zfar: quasars at (z≈≈6.4) and GRBs (z6.4) and GRBs (z≈8.2)≈8.2)

(SDSS image; taken in October 2003)

(Swift image; GRB 090423A)

A large redshift z implies ...A large redshift z implies ...

The spectrum is strongly shifted toward red or even The spectrum is strongly shifted toward red or even infrared colorsinfrared colors

The object is very far awayThe object is very far away We see the object at an epoch when the universe We see the object at an epoch when the universe

was much younger than the present day universewas much younger than the present day universe most distant astrophysical object discovered so far: most distant astrophysical object discovered so far:

z = 8.2z = 8.2 z z ≳ ≳ 9: “dark ages”9: “dark ages”

Can we calculate a(t) ?Can we calculate a(t) ?

FFoutsideoutside= 0= 0

Hubble RadiusHubble Radius

distant galaxydistant galaxy

Can we calculate a(t) ?Can we calculate a(t) ?

2R

mMGF galinside

inside 2R

mMGF galinside

inside

What is the future of that galaxy ?What is the future of that galaxy ?

Critical velocity: escape speedCritical velocity: escape speed

v<vv<vescesc: galaxy eventually stops and falls back: galaxy eventually stops and falls back

v>vv>vescesc: galaxy will move away forever: galaxy will move away forever

a

MGv inside

esc

2

a

MGv inside

esc

2

Let’s rewrite that a bit ...Let’s rewrite that a bit ...

<0 v<vesc: galaxy eventually stops and : galaxy eventually stops and

falls backfalls back >0 v>vesc: galaxy will move away forever: galaxy will move away forever

222

a

MGv inside

222

a

MGv inside

222

a

MGv inside

222

a

MGv inside

2

3

8 22 aG

v 2

3

8 22 aG

v

Let’s rewrite that a bit ...Let’s rewrite that a bit ...

Homogeneous sphere of density Homogeneous sphere of density ::

so for the velocity:so for the velocity:

but what is but what is ? ?

3

3

4aM inside

3

3

4aM inside

Let’s switch to general relativityLet’s switch to general relativity

Friedmann equationFriedmann equation

same same k as in the Robertson-Walker metric as in the Robertson-Walker metric

222

3

8kca

Gv 222

3

8kca

Gv

222222

2222 sin

1)( rr

kr

rtatcs

222222

2222 sin

1)( rr

kr

rtatcs

Let’s switch to general relativityLet’s switch to general relativity

Friedmann equationFriedmann equation

k k is the curvature constantis the curvature constant• k=0k=0: flat space, forever expanding: flat space, forever expanding

• k>0k>0: spherical geometry, eventually recollapsing: spherical geometry, eventually recollapsing

• k<0k<0: hyperbolic geometry, forever expanding: hyperbolic geometry, forever expanding

222

3

8kca

Gv 222

3

8kca

Gv

222

3

8kca

Gv 222

3

8kca

Gv

2

2

2

2

3

8

a

kcG

a

v

2

2

2

2

3

8

a

kcG

a

v

Can we predict the fate of the Universe ?Can we predict the fate of the Universe ?

Friedmann equation:Friedmann equation:

2

2

2

220 3

8

a

kcG

a

vH

2

2

2

220 3

8

a

kcG

a

vH

k=0k=0::

G

Hcrit

8

3 20

G

Hcrit

8

3 20

Can we predict the fate of the Universe ?Can we predict the fate of the Universe ?

If the density If the density of the Universe of the Universe =crit:: flat space, forever expandingflat space, forever expanding

>crit:: spherical geometry, recollapsingspherical geometry, recollapsing

< crit:: hyperbolic geometry, forever expandinghyperbolic geometry, forever expanding

so what is the density of the universe?so what is the density of the universe?• We don’t know preciselyWe don’t know precisely >crit very unlikelyvery unlikely

• currently favored modelcurrently favored model: : 0.3crit

k>0k>0 k<0k<0k=0k=0

How big is How big is critcrit ? ?

critcrit == 881010-30-30 g/cmg/cm33 1 atom per 200 liter 1 atom per 200 liter

Density parameterDensity parameter 00 ::

00 =1 =1:: flat space, forever expanding (open)flat space, forever expanding (open)

00 >1 >1:: spherical geometry, recollapsing (closed)spherical geometry, recollapsing (closed)

00 <1 <1:: hyperbolic geometry, forever expandinghyperbolic geometry, forever expanding

Currently favored model:Currently favored model: 00 = 0.3 = 0.3

G

H

crit

8

3 20

0 G

H

crit

8

3 20

0

““Observational cosmology”: The quest for Observational cosmology”: The quest for three numbers !three numbers !

The Hubble constant The Hubble constant HH00

how fast is the universe expandinghow fast is the universe expanding The density parameter The density parameter 00

how much mass is in the universehow much mass is in the universe The cosmological constant The cosmological constant

the vacuum energy of the universethe vacuum energy of the universe

(or the “deceleration parameter” (or the “deceleration parameter” qq0 0 , which is a , which is a

combination of the others)combination of the others)

Observational Tests and Observational Tests and PredictionsPredictions








1. Measuring 1. Measuring HH00

Distances in the local universeDistances in the local universe

Assume a linear expansion (Assume a linear expansion (Hubble law): Hubble law): v=cz=Hv=cz=H00·D·D

Use the distance modulus Use the distance modulus m-M=5m-M=5loglog(D/10pc)-5(D/10pc)-5

Distances of a ‘standard candle’ (Distances of a ‘standard candle’ (M=const.M=const.) or ) or calibrated ‘standard candle’ calibrated ‘standard candle’ m=5m=5loglog(z)+b (z)+b b = M+25+5b = M+25+5loglog(c)-5(c)-5loglog(H(H00))

Distances with Distances with δδ Cephei stars Cephei stars

Direct measurement of the change in angular diameterDirect measurement of the change in angular diameter

plus spectroscopic radial velocity (Kervella et al. 2004)plus spectroscopic radial velocity (Kervella et al. 2004)


LMC LMC CepheidsCepheids


NGC 300 NGC 300 CepheidsCepheids

(~ 6MLy)(~ 6MLy)

(Gieren et al. (Gieren et al. 2006)2006)


(Freedman et al. 1994)(Freedman et al. 1994)

Distances with Type Ia SupernovaeDistances with Type Ia Supernovae

Use the Hubble diagram (Use the Hubble diagram (m-Mm-M vs.vs. log log zz)) m-M=5m-M=5loglog(z)+25+5(z)+25+5loglog(c)-5(c)-5loglog(H(H00))

Note that the slope is given here.Note that the slope is given here. Hubble constant can be derived when the Hubble constant can be derived when the

absolute luminosity absolute luminosity MM is known is known loglogHH00==loglog(z)+5+(z)+5+loglog(c)-0.2(m-M)(c)-0.2(m-M)

Hubble constant from SNe IaHubble constant from SNe Ia

Calibrate the absolute luminosityCalibrate the absolute luminosity• through Cepheidsthrough Cepheids

‘‘classical distance ladder’classical distance ladder’• depends on the accuracy of the previous rungs on the ladderdepends on the accuracy of the previous rungs on the ladder

• LMC distance, P-L(-C) relation, metallicitiesLMC distance, P-L(-C) relation, metallicities HST program (Sandage, Tammann)HST program (Sandage, Tammann) HST Key Programme (Freedman, Kennicutt, Mould, HST Key Programme (Freedman, Kennicutt, Mould,

Madore)Madore)

• through modelsthrough models extremely difficult (but possible!)extremely difficult (but possible!)

Absolute Magnitudes of SNe IaAbsolute Magnitudes of SNe Ia

SN Galaxy m-M MB MV MIm15

1937C IC 4182 28.36 (12) -19.56 (15) -19.54 (17) - 0.87 (10)1960F NGC 4496A31.03 (10) -19.56 (18) -19.62 (22) - 1.06 (12)1972E NGC 5253 28.00 (07) -19.64 (16) -19.61 (17) -19.27 (20)0.87 (10)1974G NGC 4414 31.46 (17) -19.67 (34) -19.69 (27) - 1.11 (06)1981B NGC 4536 31.10 (12) -19.50 (18) -19.50 (16) - 1.10 (07)1989B NGC 3627 30.22 (12) -19.47 (18) -19.42 (16) -19.21 (14)1.31 (07)1990N NGC 4639 32.03 (22) -19.39 (26) -19.41 (24) -19.14 (23)1.05 (05)1998bu NGC 3368 30.37 (16) -19.76 (31) -19.69 (26) -19.43 (21)1.08 (05)1998aq NGC 3982 31.72 (14) -19.56 (21) -19.48 (20) - 1.12 (03)Straight mean -19.57 (04) -19.55 (04) -19.26 (0 6)Weighted mean -19.56 (07) -19.53 (06) -19.25 (0 9)

(Saha et al. 1999)(Saha et al. 1999)

Nearby SNe IaNearby SNe Ia

Phillips et al. (1999)

Light curve shape – luminosityLight curve shape – luminosity

((B-band light curves; Calan/Tololo sample, Kim et al. 1997)B-band light curves; Calan/Tololo sample, Kim et al. 1997)

After calibrationAfter calibration:: SNe Ia look like good “standard SNe Ia look like good “standard candles”!candles”!

Normalisation of the peak luminosityNormalisation of the peak luminosity

Using the Using the luminosity-decline luminosity-decline rate relation one can rate relation one can normalise the peak normalise the peak luminosity of SNe Ialuminosity of SNe Ia

Phillips et al. 1999

Reduces the scatter!

The nearby SN Ia sampleThe nearby SN Ia sample

Evidence for gooddistances








Hubble constant from SNe Ia Hubble constant from SNe Ia

Extremely good (relative) distance indicatorsExtremely good (relative) distance indicators• distance accuracy better than 10%distance accuracy better than 10%

Uncertainty in HUncertainty in H00 mostly from the LMC and mostly from the LMC and

the Cepheid P-L relationthe Cepheid P-L relation Today’s best value (Cepheids + SNe Ia):Today’s best value (Cepheids + SNe Ia):

HH00 = (72 ± 7) km/s/Mpc = (72 ± 7) km/s/Mpc

Note:Note: This enters as an uncertainty in many other This enters as an uncertainty in many other places! places!

2. Measuring 2. Measuring ΩΩ00 and q and q00

How can we measure How can we measure 00 ? ?

Count all the mass we can “see”Count all the mass we can “see”• tricky, some of the mass may be hidden …tricky, some of the mass may be hidden …

Measure the rate at which the expansion of the Measure the rate at which the expansion of the universe is slowing downuniverse is slowing down• a more massive universe will slow down fastera more massive universe will slow down faster

Measure the geometry of the universeMeasure the geometry of the universe• is it spherical, hyperbolic or flat ?is it spherical, hyperbolic or flat ?

(Most accurate: CMB !)(Most accurate: CMB !)

Let’s try to measure the decelerationLet’s try to measure the deceleration

Acceleration according to Newton:Acceleration according to Newton:

Deceleration parameterDeceleration parameter

aG

a

MGa

3

42

a

G

a

MGa

3

42

20

20

v

aaq

2

020

v

aaq

((Note:Note: This is without a This is without a ΛΛ-term!)-term!)

So what’s the meaning of So what’s the meaning of qq00 ? ?

Deceleration parameter Deceleration parameter qq00

• q0>0.5: deceleration is so strong that deceleration is so strong that

eventually the universe stops eventually the universe stops expanding and starts collapsingexpanding and starts collapsing

• 0<q0<0.5: deceleration is too weak to stop deceleration is too weak to stop

the expansionthe expansion

What’s the difference between What’s the difference between q0, 0 and and k ??

• k: curvature of the universecurvature of the universe0: mass content of the universemass content of the universe

• q0: kinematics of the universe kinematics of the universe

So let’s measure So let’s measure qq0 0 ! !

How do we do that?How do we do that?• Measure the rate of expansion at different times, Measure the rate of expansion at different times,

i.e. measure and compare the expansion based on i.e. measure and compare the expansion based on nearby galaxies and based on high redshift galaxies nearby galaxies and based on high redshift galaxies or other objects, e.g., Type Ia supernovae.or other objects, e.g., Type Ia supernovae.

Gravity is slowing down the expansion Gravity is slowing down the expansion expansion rate should be higher at high expansion rate should be higher at high redshift. redshift.

Supernovae Supernovae are very rare, ~ are very rare, ~ 1 SN per 100 1 SN per 100 years and years and galaxy. galaxy.

One has to One has to observe very observe very many galaxies!many galaxies!

Very distant supernovaeVery distant supernovae

Search strategy:Search strategy:

1.1. Repeated Repeated scanning of a scanning of a certain field. certain field.

2. Electronic 2. Electronic readout of the readout of the data. data.

3. Follow-up 3. Follow-up observations, observations, e.g., HST, VLT, e.g., HST, VLT, ……

Supernovae are Supernovae are routinely routinely detected at detected at redshifts Z > 0.1: redshifts Z > 0.1:

What is the What is the intrinsic scatter intrinsic scatter in luminosities?in luminosities?

Are they different Are they different from the local from the local sample? sample?

Do we understand Do we understand

the the differences?differences?

So let’s measure So let’s measure qq0 0 !!

qq00 = 0 = 0qq00 = 0.5 = 0.5

more distantmore distant

fain

ter

fain

ter

Data indicates:Data indicates:

qq00 < 0 < 0

Expansion Expansion

is acceleratingis accelerating

Science discovery of the year 1998Science discovery of the year 1998

The expansion of the The expansion of the universe is accelerating !!!universe is accelerating !!!

But gravity is always But gravity is always attractive, so it only can attractive, so it only can deceleratedecelerate

→→ Revival of the Revival of the cosmological constant cosmological constant

Friedmann’s equation for Friedmann’s equation for >0>0

k k is the curvature constantis the curvature constant• k=0k=0: flat space, flat universe: flat space, flat universe

• k>0k>0: spherical geometry, closed universe: spherical geometry, closed universe

• k<0k<0: hyperbolic geometry, open universe: hyperbolic geometry, open universe

222

3

8kca

Gv 222

3

8kca

Gv

33

8 2222 a

kcaG

v

33

8 2222 a

kcaG

v

k is the curvature constantis the curvature constant• k=0: flat space: flat space• k>0: spherical geometry: spherical geometry• k<0: hyperbolic geometry: hyperbolic geometry

but for sufficiently large but for sufficiently large a spherically curved a spherically curved universe may expand foreveruniverse may expand forever

Deceleration parameter Deceleration parameter qq for for >0>0

Acceleration according to Newton:Acceleration according to Newton:

deceleration parameterdeceleration parameter

with with

aaG

a33

4

aaG

a33

4

2

020 v

aaq

20

20 v

aaq

203H

2

03H

Mean distance between galaxies

today

fainter

Redshift

0 = 1

time

closed

0 > 1

open 0 < 1

0 = 0

- 14 - 9 - 7

Billion years

The fate of the Universe for The fate of the Universe for >0>0

Recent supernova dataRecent supernova data

Tonry et al. 2003

Very high redshift SNe IaVery high redshift SNe Ia

Riess et al. 2004

SNLS, plus BAO (Astier et al., Eisenstein SNLS, plus BAO (Astier et al., Eisenstein 2005)2005)

The “equation of state” of the The “equation of state” of the Universe: Universe: p = wρp = wρ

ä ~ (ρ + 3p)ä ~ (ρ + 3p) , , w ‹ -1/3 w ‹ -1/3 ::

accelerationacceleration!!

w 0.969 0.061(stat) 0.065(sys)

w 1.0010.071(stat) 0.081(sys)

SNeSNe + + BAOBAO + + CMBCMB

... and allowing for curvature: ... and allowing for curvature:

(Kowalski (Kowalski 2009)2009)

Best determinations Best determinations today:today:

The “constitution” data set (M. Kowalski)The “constitution” data set (M. Kowalski)

© S.Benitez© S.Benitez

… … and fitsand fits

to the datato the data

© S.Benitez© S.Benitez

Is the fate of the Universe well determined ?Is the fate of the Universe well determined ?

deceleration:deceleration:• ½½00 – – > 0> 0: decelerating: decelerating

• ½½00 – – < 0< 0: accelerating: accelerating

curvaturecurvature00 + + = 1= 1: flat: flat

00 + + < 1< 1: hyperbolic: hyperbolic

00 + + > 1> 1: spherical: spherical

two equations for two variables two equations for two variables well posed well posed problem (for constant problem (for constant ΛΛ))

Observational cosmology: the quest for three Observational cosmology: the quest for three numbers !numbers !


• how fast is the universe expandinghow fast is the universe expanding

The density parameter The density parameter 00

• how much mass is in the universehow much mass is in the universe

The cosmological constant The cosmological constant

• the vacuum energy of the universethe vacuum energy of the universe Current observational situation:Current observational situation:

• HH00 ≈≈ 72 km/s/Mpc 72 km/s/Mpc

00 ≈≈0.30.3;; ≈≈ 0.7 0.7 flat space!flat space!

The age of the Universe revisitedThe age of the Universe revisited

So far, we have assumed that the expansion So far, we have assumed that the expansion velocity is not changing (velocity is not changing (qq00=0=0, empty , empty

universe)universe) How does this How does this

estimate change, estimate change, if the expansion if the expansion decelerates, i.e. decelerates, i.e. qq00>0 >0 ??

An An 00>0>0, , =0=0 universe is younger than 14 Gyr universe is younger than 14 Gyr

now

now


So far, we only have considered decelerating So far, we only have considered decelerating universesuniverses

How does this How does this estimate change, estimate change, if the expansion if the expansion accelerates, i.e. accelerates, i.e. qq00<0 <0 ??

An An >0>0 universe can be older than 14 Gyr universe can be older than 14 Gyr


00=0=0, , =0=0: : ttHubbleHubble ==1/1/HH00 ≈≈ 14 Gyr 14 Gyr

00=1=1, , =0=0: : ttHubbleHubble ==2/(32/(3HH00) ) ≈≈ 10 Gyr 10 Gyr

Open universes with Open universes with 0<0<00<1<1, , =0 =0 are are

between 10 and 14 Gyr oldbetween 10 and 14 Gyr old Closed universes with Closed universes with 00>1>1, , =0 =0 are less are less

than 10 Gyr oldthan 10 Gyr old >0 >0 increases, increases, <0 <0 decreases the age of the decreases the age of the

universeuniverse 00=0.3=0.3, , =0.7=0.7: : ttHubbleHubble ==0.96/0.96/HH00 ≈≈ 13.7 Gyr13.7 Gyr

At early epochs, the first term dominatesAt early epochs, the first term dominates the early universe appears to be almost flatthe early universe appears to be almost flat

At late epochs, the second term dominatesAt late epochs, the second term dominates the late universe appears to be almost emptythe late universe appears to be almost empty

2

2

3

8

a

kcGH

2

2

3

8

a

kcGH

Friedmann’s equation for Friedmann’s equation for =0, =0, 00<1<1

Expansion rateExpansion rate

of the Universeof the UniverseFalls off like Falls off like

the cube of Rthe cube of R

Falls off like Falls off like

the square of Rthe square of R

At early epochs, the first term dominatesAt early epochs, the first term dominates the early universe appears to be almost flatthe early universe appears to be almost flat

At late epochs, the third term dominatesAt late epochs, the third term dominates the late universe appears to be exponentially the late universe appears to be exponentially

expandingexpanding

33

82

2

a

kcGH

33

82

2

a

kcGH

Friedmann’s equation for Friedmann’s equation for >0, >0, 00<1<1

Expansion rateExpansion rate

of the Universeof the UniverseFalls off like Falls off like

the cube of Rthe cube of RFalls off like Falls off like

the square of Rthe square of R

constantconstant

A puzzling detailA puzzling detail

=0=0: for most of its age, the universe looks either to : for most of its age, the universe looks either to be flat or to be emptybe flat or to be empty

>0>0: for most of its age, the universe looks either to : for most of its age, the universe looks either to be flat or to be exponentially expandingbe flat or to be exponentially expanding

Isn’t it strange that we appear to live in that short Isn’t it strange that we appear to live in that short period between those two extremes period between those two extremes

=>=> Flatness problem ! Flatness problem !

3. The cosmic microwave 3. The cosmic microwave backgroundbackground

A quote ...A quote ...

John Bahcall: John Bahcall: "The discovery of the cosmic "The discovery of the cosmic microwave background radiation changed microwave background radiation changed forever the nature of cosmology, from a subject forever the nature of cosmology, from a subject that had many elements in common with that had many elements in common with theology to a fantastically exciting empirical theology to a fantastically exciting empirical study of the origins and evolution of the things study of the origins and evolution of the things that populate the physical universe."that populate the physical universe."

The cosmic microwave background radiation The cosmic microwave background radiation (CMB)(CMB)

Temperature of Temperature of 2.728±0.004 K2.728±0.004 K

Isotropic to Isotropic to 1 part in 100 0001 part in 100 000

Perfect black bodyPerfect black body 1990ies: CMB is 1990ies: CMB is

one of the major tools to study cosmologyone of the major tools to study cosmology Note: ~1% of the noise in your TV is from Note: ~1% of the noise in your TV is from

the big bangthe big bang

Nobel Price in Physics 2006 for COBE:Nobel Price in Physics 2006 for COBE:

John MatherJohn Mather

George SmootGeorge Smoot

The Cosmic Background Explorer (COBE) The Cosmic Background Explorer (COBE) (1989 - 1993)(1989 - 1993)

Main objectives:Main objectives: To accurately To accurately

measure the measure the temperature of the temperature of the CMBCMB

To find the To find the expected expected fluctuations in the fluctuations in the CMBCMB

Interpretation of the results from the COBE)Interpretation of the results from the COBE)

The Earth is moving The Earth is moving with respect to the with respect to the CMB CMB Doppler shift Doppler shift

The emission of the The emission of the GalaxyGalaxy

Fluctuations in the Fluctuations in the CMBCMB

Measuring the Curvature of the Universe Measuring the Curvature of the Universe Using the CMBUsing the CMB

Result fromResult from Boomerang Boomerang (1998):(1998):

The Universe is The Universe is flat to within flat to within 10%!10%!

Measuring the Curvature of the Universe Measuring the Curvature of the Universe Using the CMBUsing the CMB

Recall: with Recall: with supernovae, one supernovae, one measures measures qq00 =½ =½00 – –

CMB fluctuations CMB fluctuations measure curvaturemeasure curvature 00 + +

two equations for two equations for two variablestwo variables problem solved problem solved

Interpretation of the dataInterpretation of the data

(CMB + BAO + SNe) :(CMB + BAO + SNe) :

Geometry : “flat” (Euklidian)

Ω0 = 1.0052 ± 0.0064

“Dark Energy”:

ΩΛ = 0.721 ± 0.015

“Dark Matter”:

ΩD = 0.233 ± 0.013

Baryons:

ΩB = 0.0462± 0.0015

Age of the Universe:

13.73 ± 0.12 GyrsThat’s precision cosmology!That’s precision cosmology!

4. Primordial nucleosynthesis4. Primordial nucleosynthesis

Until mid 60ies: big bang model very Until mid 60ies: big bang model very controversial, many alternative modelscontroversial, many alternative models

After mid 60ies: little doubt on validity of After mid 60ies: little doubt on validity of the big bang modelthe big bang model

Four pillars on which the big bang theory is Four pillars on which the big bang theory is resting:resting:• Hubble’s law Hubble’s law • Cosmic microwave background radiationCosmic microwave background radiation• The origin of the elementsThe origin of the elements• Structure formation in the universeStructure formation in the universe

General acceptance of the big bang modelGeneral acceptance of the big bang model



Four pillars on which the big bang theory is Four pillars on which the big bang theory is resting:resting:• Hubble’s law Hubble’s law • Cosmic microwave background radiation Cosmic microwave background radiation • The origin of the elements The origin of the elements ←←

• Structure formation in the universeStructure formation in the universe

Georgy Gamov (1904-1968)Georgy Gamov (1904-1968)

If the universe is expanding, then If the universe is expanding, then there has been a big bangthere has been a big bang

Therefore, the early universe must Therefore, the early universe must have been very dense and hothave been very dense and hot

Optimum environment to breed the elements by Optimum environment to breed the elements by nuclear fusion (Alpher, Bethe & Gamow, 1948)nuclear fusion (Alpher, Bethe & Gamow, 1948)• success: predicted that helium abundance is 25%success: predicted that helium abundance is 25%

• failure: could not reproduce elements more massive failure: could not reproduce elements more massive than lithium and beryllium (than lithium and beryllium ( formed in stars) formed in stars)

Abundances of elementsAbundances of elements

Hydrogen Hydrogen and helium and helium most most abundantabundant

gap around gap around Li, Be, BLi, Be, B

Thermal history of the universeThermal history of the universe

When the universe was younger than When the universe was younger than 300 000 yrs, it was so hot that neutral atoms 300 000 yrs, it was so hot that neutral atoms separated into nuclei and electrons. It was too separated into nuclei and electrons. It was too hot to bind atomic nuclei and electrons to hot to bind atomic nuclei and electrons to atoms by the electromagnetic force atoms by the electromagnetic force

When the universe was younger than When the universe was younger than ~1 sec, it was so hot that atom nuclei separated ~1 sec, it was so hot that atom nuclei separated into neutrons and protons. It was too hot to into neutrons and protons. It was too hot to bind protons and neutrons to atomic nuclei by bind protons and neutrons to atomic nuclei by the strong nuclear force the strong nuclear force

Transforming hydrogen into heliumTransforming hydrogen into helium

Hot big bang: Hot big bang: neutronsneutrons and and protonsprotons Use a multi step procedure:Use a multi step procedure:

• p + n p + n 22H H

• p + p + 22H H 33HeHe

• n + n + 22H H 33HH

• 33He + He + 33He He 44He + 2 pHe + 2 p some side reactions:some side reactions:

• 44He + He + 33H H 77Li Li

• 44He + He + 33He He 77Be Be

Mass gap/stability gap at A=5 and 8Mass gap/stability gap at A=5 and 8

There is no stable atomic nucleus with 5 or There is no stable atomic nucleus with 5 or with 8 nucleonswith 8 nucleons

Reaction chain stops at Reaction chain stops at 77LiLi So how to form the more massive elements?So how to form the more massive elements? There exist a meta-stable nucleus (There exist a meta-stable nucleus (88B*B*). If ). If

this nucleus is hit by another this nucleus is hit by another 44HeHe during its during its lifetime, lifetime, 1212CC and other elements can be and other elements can be formedformed

Mass gap/stability gap at A=5 and 8Mass gap/stability gap at A=5 and 8

Reaction chain:Reaction chain:

• 44He + He + 44He He 88B* B*

• 88B* + B* + 44He He 1212CC so-called 3-body reactionso-called 3-body reaction in order to have 3-body reactions, high particle in order to have 3-body reactions, high particle

densities are requireddensities are required

• densities are not high enough in the big-bangdensities are not high enough in the big-bang

• but they are in the center of evolved starsbut they are in the center of evolved stars ConclusionConclusion: big bang synthesizes elements up to : big bang synthesizes elements up to

77Li. Higher elements are formed in starsLi. Higher elements are formed in stars

Primordial nucleosynthesisPrimordial nucleosynthesis


Result:Result: abundances abundances

of H, He of H, He and Li are and Li are consistentconsistent

but:but: bb

~0.04~0.04

Consistent with Consistent with

abundanceabundance

of H, He and Liof H, He and Li


CMB:CMB: ΩΩbb h h22 = 0.0225 ± 0.0006 = 0.0225 ± 0.0006

Perfect agreement!Perfect agreement!

ButBut: :

The Li problem!The Li problem!

Can we understand why 25% He?Can we understand why 25% He?

Before the universe cooled sufficiently to Before the universe cooled sufficiently to allow nucleons to assemble into helium, the allow nucleons to assemble into helium, the neutron to proton ratio was ~1:7neutron to proton ratio was ~1:7

44He:He: equal number of protons and neutrons equal number of protons and neutrons Assume that all neutrons grab a proton to Assume that all neutrons grab a proton to

form a form a 44HeHe. The left over protons form . The left over protons form hydrogen.hydrogen.

n

nnX n

H

*2 75.0

7/8

7/6

/1

/1*2

pn

pn

np

npnH nn

nn

nn

nn

n

nnX

Can we understand why 25% He?Can we understand why 25% He?

Abundance of hydrogenAbundance of hydrogen Abundance of hydrogenAbundance of hydrogen

Abundance of helium: Abundance of helium: 11- - 0.75 = 0.250.75 = 0.25 butbut why is why is nnnn/n/npp ≈≈ 1/7 1/7 ? ?

The four forces of natureThe four forces of nature

GravityGravity• weak, long rangedweak, long ranged

electromagnetismelectromagnetism• intermediate, long rangedintermediate, long ranged

strong nuclear forcestrong nuclear force• strong, short rangedstrong, short ranged

weak nuclear forceweak nuclear force• weak, short rangedweak, short ranged

The weak nuclear forceThe weak nuclear force

n n p p++ + e + e- - + + νν

+ n + n ↔↔ p p++ + e + e--

Free neutrons decay into protonsFree neutrons decay into protons

n : neutronn : neutron pp+ + : proton: proton ee- - : electron: electron : neutrino: neutrino neutron half life: 10 minneutron half life: 10 min

Baryons Baryons Hadrons Hadrons

LeptonsLeptons

}}

}}

kT

Δmcexp

n

n 2

p

n

““Freeze out” of weak equilibriumFreeze out” of weak equilibrium

4

Neutron/proton ratioNeutron/proton ratio

Freeze-out temperature: Freeze-out temperature: kT ~ 700 - 800 keVkT ~ 700 - 800 keV Mass difference:Mass difference: ΔΔmcmc2 2 = 1.293 MeV= 1.293 MeV nnnn/n/npp ≈1/6≈1/6 20% of the neutrons decay after 200 s20% of the neutrons decay after 200 s

nnnn/n/npp ≈ 1/7 ≈ 1/7

Break!Break!

Formation of large-scale Formation of large-scale structure (and galaxies)structure (and galaxies)

Web address for movies:Web address for movies:

http://www.mpa-garching.mpg.de/~wfh/http://www.mpa-garching.mpg.de/~wfh/

General acceptance of the big bang modelGeneral acceptance of the big bang model



Four pillars on which the big bang theory is Four pillars on which the big bang theory is resting:resting:• Hubble’s law Hubble’s law • Cosmic microwave background radiation Cosmic microwave background radiation • The origin of the elementsThe origin of the elements • Structure formation in the universe Structure formation in the universe ←←

Structure formation in the Big-Bang modelStructure formation in the Big-Bang model

A galaxy censusA galaxy census

How good is the assumption of isotropy?How good is the assumption of isotropy?

CMB: almost CMB: almost perfectperfect

But what about But what about the closer the closer neighborhood ?neighborhood ?

How good is the assumption of isotropy?How good is the assumption of isotropy?

CMB: almost CMB: almost perfectperfect

But what about But what about the closer the closer neighborhood ?neighborhood ?

The “great wall”

Galaxies are not randomly distributed but correlatedGalaxies are not randomly distributed but correlated Network of structures (filaments, sheets, walls) Network of structures (filaments, sheets, walls)

“cosmic web”“cosmic web”

The spatial distribution of galaxiesThe spatial distribution of galaxies

Data from the Data from the most recent most recent survey:survey:

SDSSSDSS

The spatial distribution of galaxiesThe spatial distribution of galaxies

How does structure form ?How does structure form ?

Wrinkles in the CMB: regions of higher and Wrinkles in the CMB: regions of higher and lower temperaturelower temperature

Those regions correspond to Those regions correspond to density density fluctuationsfluctuations, regions of slightly higher/lower , regions of slightly higher/lower density than averagedensity than average

Gravitational instabilityGravitational instability• higher density higher density more mass in a given volume more mass in a given volume

• more mass more mass stronger gravitational attraction stronger gravitational attraction

• stronger gravitational attraction stronger gravitational attraction mass is mass is pulled in pulled in even higher density even higher density

z=9.00z=9.00

65 M

pc65

Mpc

50 million 50 million particle particle N-body N-body simulationsimulation

z=4.00z=4.00

65 M

pc65

Mpc


z=2.33z=2.33

65 M

pc65

Mpc


z=1.00z=1.00

65 M

pc65

Mpc


z=0.00z=0.00

65 M

pc65

Mpc


Does a picture like this look familiar ?Does a picture like this look familiar ?

Recent simulations (MPA group)Recent simulations (MPA group)

(Court. V. Springel)(Court. V. Springel)

Recent simulations (MPA group)Recent simulations (MPA group)


Note:Note: The simulations assume that most of the The simulations assume that most of the

matter in the Universe is non-baryonic and matter in the Universe is non-baryonic and “dark”!“dark”!

Q: What is it ?Q: What is it ?

A: MACHOs or WIMPsA: MACHOs or WIMPs

MACHOs ?MACHOs ?

MAMAssive ssive CCompact ompact HHalo alo OObjectsbjects Brown dwarfs (stars not massive enough to Brown dwarfs (stars not massive enough to

shine)shine) Dim white dwarfs (relics of stars like the Dim white dwarfs (relics of stars like the

Sun)Sun) Massive black holes (stars that massive that Massive black holes (stars that massive that

even light cannot escape)even light cannot escape) But: But: if the DM is really in MACHOs, if the DM is really in MACHOs,

something with the nucleosynthesis something with the nucleosynthesis constraint must be wrongconstraint must be wrong

How can we see MACHOs ?How can we see MACHOs ?

Gravitational lensing:Gravitational lensing:

If foreground object has only little mass, the If foreground object has only little mass, the image split is too small to be observedimage split is too small to be observed

But the amplification (brightening) is observableBut the amplification (brightening) is observable

How can we see MACHOs ?How can we see MACHOs ? How likely is it for a star in the Milky Way to get How likely is it for a star in the Milky Way to get

amplified ?amplified ? Once every 10 million years !!!Once every 10 million years !!!

How did this work ?How did this work ?

Monitor 10 million stars simultaneously !Monitor 10 million stars simultaneously !

Light curve of a MACHO eventLight curve of a MACHO event

Achromatic (!) Achromatic (!) magnification due to magnification due to gravitational lensinggravitational lensing

There seem to be There seem to be not enough brown not enough brown dwarfs (or dark dwarfs (or dark objects of similar objects of similar mass) to account mass) to account for the dark matter for the dark matter in the Milky Way !in the Milky Way !

WIMPs ?WIMPs ?

WWeakly eakly IInteracting nteracting MMassive assive PParticlesarticles Massive neutrinos Massive neutrinos

• at least we know that they existat least we know that they exist

• their masses seem to be lowtheir masses seem to be low

• they would be they would be hot dark matterhot dark matter ( (hot: moving at hot: moving at speeds near the speed of light) speeds near the speed of light)

Another (yet undiscovered) particle Another (yet undiscovered) particle predicted by some particle physicistspredicted by some particle physicists• cold dark mattercold dark matter (cold: moving much slower (cold: moving much slower

than the speed of light)than the speed of light)

WIMP candidate I: Massive neutrinosWIMP candidate I: Massive neutrinos

What mass do we need to account for all the What mass do we need to account for all the dark matter ?dark matter ?• There areThere are ~100 ~100 neutrinos per cmneutrinos per cm33

• A mass ofA mass of 20eV 20eV results inresults in 00=0.3 =0.3

Can we measure their mass ?Can we measure their mass ?• tricky …tricky …

• use energy conservation. Measure all masses and use energy conservation. Measure all masses and velocities in the velocities in the + n + n p p++ + e + e- - reaction with high reaction with high precision. Difference between left and right hand precision. Difference between left and right hand side side neutrino mass neutrino mass

Direct measurements:Direct measurements: ββ decays decays

Best value to date:Best value to date:

mm≤4eV≤4eV

The KamLAND detector:The KamLAND detector:

Neutrino oscillationsNeutrino oscillations

WIMP candidate I: Massive neutrinosWIMP candidate I: Massive neutrinos

Result: No clear (direct) detection, but upper Result: No clear (direct) detection, but upper limits. The mass of the (electron) neutrino is limits. The mass of the (electron) neutrino is (much?) (much?) less than a few eV less than a few eV electron neutrino is electron neutrino is ruled out ruled out as a dark matter candidate.as a dark matter candidate.

There are There are two more two more neutrino families, neutrino families, μμ neutrinosneutrinos and and ττ neutrinos neutrinos (the (the muonmuon and and tauontauon are particles are particles similar to the electron, but more massive and similar to the electron, but more massive and unstable). unstable).

But: But: Their masses seem to be not too different Their masses seem to be not too different from from ννee’s’s

WIMP candidate II: The least massive WIMP candidate II: The least massive supersymmetric particlesupersymmetric particle

Main goal of particle physics: to develop a theory Main goal of particle physics: to develop a theory that unifies the four forces of naturethat unifies the four forces of nature

Those models predict a whole zoo of particles, Those models predict a whole zoo of particles, some of them are already detected, but most of some of them are already detected, but most of them still very speculative. Most of these particles them still very speculative. Most of these particles are unstable.are unstable.

Supersymmetry is a particularly promising Supersymmetry is a particularly promising unifying theoryunifying theory

The least massive supersymmetric particle The least massive supersymmetric particle (neutralino) should be stable(neutralino) should be stable

WIMP candidate II: The least massive WIMP candidate II: The least massive supersymmetric particlesupersymmetric particle

It’s mass should be > 150 GeV, otherwiseIt’s mass should be > 150 GeV, otherwise• its contribution would be irrelevantits contribution would be irrelevant

• it should already have been detectedit should already have been detected But how to prove its existence ?But how to prove its existence ?

How can we find cold WIMPs ?How can we find cold WIMPs ?

Cryogenic (ultra cold) detectorsCryogenic (ultra cold) detectors Search for annual modulation of the signal Search for annual modulation of the signal

Do we have already detected WIMPs ?Do we have already detected WIMPs ?

Results are very controversial and inconclusiveResults are very controversial and inconclusive

DAMADAMA

collabor-collabor-

ationation

Can astronomy help to discriminate between Can astronomy help to discriminate between neutrinos and neutralinos ?neutrinos and neutralinos ?

Neutrinos:Neutrinos:• mass in the tens of eV mass in the tens of eV very low mass very low mass

• very low mass very low mass high velocities high velocities “hot” “hot”

• can travel several tens of Mpc over the age of the can travel several tens of Mpc over the age of the universeuniverse

NeutralinosNeutralinos• mass in the hundredst of GeV mass in the hundredst of GeV very high mass very high mass

• very high mass very high mass low velocities low velocities “cold” “cold”

• cannot travel significant distances over the age of cannot travel significant distances over the age of the universethe universe

Neutrinos: Neutrinos: Hot Dark Matter (HDM)Hot Dark Matter (HDM)• mass in the tens of eV mass in the tens of eV very low mass very low mass• very low mass very low mass high velocities high velocities “hot” “hot”• can travel several tens of Mpc over the age of the can travel several tens of Mpc over the age of the

universeuniverse Neutralinos Neutralinos Cold Dark Matter (CDM)Cold Dark Matter (CDM)

• mass in the hundredst of GeV mass in the hundredst of GeV very high mass very high mass• very high mass very high mass low velocities low velocities “cold” “cold”• cannot travel significant distances over the age of cannot travel significant distances over the age of

the universethe universe

Can astronomy help to discriminate between Can astronomy help to discriminate between hot and cold dark matter ?hot and cold dark matter ?

CDMCDM HDMHDM

Structure formation: HDM vs CDMStructure formation: HDM vs CDM

Hot dark matter:Hot dark matter:• initial small scale structure (anything smaller than initial small scale structure (anything smaller than

a galaxy cluster) washed out due to the high a galaxy cluster) washed out due to the high velocities of neutrinosvelocities of neutrinos

• clusters and supercluster form first clusters and supercluster form first

• galaxies form due to fragmentation of collapsing galaxies form due to fragmentation of collapsing clusters and superclustersclusters and superclusters

top-down structure formationtop-down structure formation


Cold dark matter:Cold dark matter:• plenty of small scale structureplenty of small scale structure

• small galaxies form first, clusters lastsmall galaxies form first, clusters last

• larger structures form due to merging of smaller larger structures form due to merging of smaller structuresstructures

bottom-up or hierarchical structurebottom-up or hierarchical structure formation formation


• CDM fits observations much better than HDMCDM fits observations much better than HDM* high-z galaxies are smallerhigh-z galaxies are smaller

* irregular shape of galaxy clusters indicate that they irregular shape of galaxy clusters indicate that they formed recentlyformed recently

* there are only a very few clusters at high redshift, there are only a very few clusters at high redshift, but many galaxiesbut many galaxies

* two-point correlation function is much better two-point correlation function is much better reproducedreproduced

A voyage through a CDM universeA voyage through a CDM universe

© M. Steinmetz© M. Steinmetz

A galaxy formation recipeA galaxy formation recipe

Ingredients: gas, radiation, gravityIngredients: gas, radiation, gravity Pick a model for the UniversePick a model for the Universe Add some seeds (perturbations) to Add some seeds (perturbations) to

trigger growth of structuretrigger growth of structure Combine it with some recipe of your Combine it with some recipe of your

star formation cookbookstar formation cookbook

(Courtesy: M. Steinmetz)

(Courtesy: M. Steinmetz)


Hierarchical galaxy formationHierarchical galaxy formation

Phase I: Formation of First Galactic Disks (1Gyr)Phase I: Formation of First Galactic Disks (1Gyr)Phase I: Formation of First Galactic Disks (1Gyr)Phase I: Formation of First Galactic Disks (1Gyr)

first relaxed small disksfirst relaxed small disks first relaxed small disksfirst relaxed small disks

Phase II: Bulge Formation and Disk Reassembly (2 Gyr)Phase II: Bulge Formation and Disk Reassembly (2 Gyr)Phase II: Bulge Formation and Disk Reassembly (2 Gyr)Phase II: Bulge Formation and Disk Reassembly (2 Gyr)

Disks are destroyed by merging, formation of an Disks are destroyed by merging, formation of an ellipticalelliptical

Later on: disk reassembleLater on: disk reassemble

Disks are destroyed by merging, formation of an Disks are destroyed by merging, formation of an ellipticalelliptical

Later on: disk reassembleLater on: disk reassemble

Phase III: Well Developed Disk+Bulge Structure (3 Gyr)Phase III: Well Developed Disk+Bulge Structure (3 Gyr)Phase III: Well Developed Disk+Bulge Structure (3 Gyr)Phase III: Well Developed Disk+Bulge Structure (3 Gyr)

slowly growing disk slowly growing disk young stars and gas in thin disk, bulge of old young stars and gas in thin disk, bulge of old

starsstars

slowly growing disk slowly growing disk young stars and gas in thin disk, bulge of old young stars and gas in thin disk, bulge of old

starsstars

Phase IV: Tidally Triggered Bar Formation (5 Gyr)Phase IV: Tidally Triggered Bar Formation (5 Gyr)Phase IV: Tidally Triggered Bar Formation (5 Gyr)Phase IV: Tidally Triggered Bar Formation (5 Gyr)

several minor mergers several minor mergers rapidly rotating barrapidly rotating bar

several minor mergers several minor mergers rapidly rotating barrapidly rotating bar

Phase V: Formation of a Giant Elliptical (7 Gyr)Phase V: Formation of a Giant Elliptical (7 Gyr)Phase V: Formation of a Giant Elliptical (7 Gyr)Phase V: Formation of a Giant Elliptical (7 Gyr)

nuclear star burst consumes nearly all remaining nuclear star burst consumes nearly all remaining gasgas

nuclear star burst consumes nearly all remaining nuclear star burst consumes nearly all remaining gasgas

SummarySummary

© Michael Turner© Michael Turner

Timeline of the UniverseTimeline of the Universe

Backed by experi-ment & observations???

Problems to be solved by quantum gravityProblems to be solved by quantum gravity

Combination of quantum mechanics and Combination of quantum mechanics and general relativitygeneral relativity

Dealing with singularities in general relativity Dealing with singularities in general relativity and particle physicsand particle physicspoint like elementary particlespoint like elementary particlesblack holesblack holesthe very early Universethe very early Universe

Nature of the Dark Energy?Nature of the Dark Energy?

Quantum cosmologyQuantum cosmology

Task:Task: calculate the wave function of the calculate the wave function of the UniverseUniverse

Problem:Problem: observer is part of the system observer is part of the system the the Copenhagen interpretation cannot be appliedCopenhagen interpretation cannot be applied

Alternative:Alternative: many-worlds interpretation many-worlds interpretation• many universes exist, but mutually unobservablemany universes exist, but mutually unobservable

• all possible outcomes are realizedall possible outcomes are realized

• whenever a decision between two (or more) states whenever a decision between two (or more) states has to be made, the universe splits into two (or has to be made, the universe splits into two (or more) branchesmore) branches

Many-worlds interpretationMany-worlds interpretation

““Close to solved” problems in cosmologyClose to solved” problems in cosmology

Present expansion rate (HPresent expansion rate (H00)) Present acceleration, geometry (not topology!) Present acceleration, geometry (not topology!)

((ΩΩ00, , qq00)) Primordial nucleosynthesisPrimordial nucleosynthesis Cosmic microwave backgroundCosmic microwave background Formation of large-scale structures and Formation of large-scale structures and

galaxiesgalaxies

Outstanding problems in cosmologyOutstanding problems in cosmology

What is the dark matter?What is the dark matter? What is the dark energy/cosmological constant?What is the dark energy/cosmological constant? Quantum gravity & Cosmology?Quantum gravity & Cosmology?

Documents

Observational Cosmology: An Introduction Wolfgang Hillebrandt MPI für Astrophysik Garching NOVICOSMO 2009 Rabac, Croatia September 20 - 30, 2009