11

Part II: Part II: Cosmological ModelsCosmological Models

& Distances& Distances[Ryden chap. 5 & 6 + a[Ryden chap. 5 & 6 + arrχχiviv papers] papers]

Miguel QuartinMiguel QuartinInstituto de Física, UFRJInstituto de Física, UFRJ

Astrofísica, Relativ. e Cosmologia (ARCOS)Astrofísica, Relativ. e Cosmologia (ARCOS)

Curso de Cosmologia Pós – 2019/1Curso de Cosmologia Pós – 2019/1

22

Chapter 5Chapter 5 Model UniversesModel Universes

Evolution of the energy densityEvolution of the energy density

Curvature–dominated universeCurvature–dominated universe

Spatially Flat modelsSpatially Flat models

Curved modelsCurved models

The Standard Model (The Standard Model (ΛΛCDM)CDM)

33

Fluid Equations ReminderFluid Equations Reminder

In Part I of our course we derived the fundamental (fluid) In Part I of our course we derived the fundamental (fluid) equations of cosmologyequations of cosmology

“Friedmann equation”

“acceleration equation”

“conservation equation”

44

Evolution of the Energy DensityEvolution of the Energy Density

The total energy density (and pressure) is just the sum of The total energy density (and pressure) is just the sum of the individual energy density (and the individual energy density (and PP) of each species) of each species

The conservation equation holds for each species The conservation equation holds for each species separately (neglecting interactions between species)separately (neglecting interactions between species)

This can be rewritten as

55

Evolution of the Energy Density (2)Evolution of the Energy Density (2)

Integrating this equation we can get Integrating this equation we can get εε((aa)) for any species for any species So far we are allowing So far we are allowing multiplemultiple species simultaneously species simultaneously

Assuming the different Assuming the different wwii to be (different) constants: to be (different) constants:

In particular for In particular for mmatter (atter (ww=0) and =0) and rradiation (adiation (ww=1/3) we get=1/3) we get

66

77

Evolution of the Energy Density (3)Evolution of the Energy Density (3) The calculation just made assumed that photons are not The calculation just made assumed that photons are not

created nor destroyedcreated nor destroyed What about emitted starlight and absorbed light?What about emitted starlight and absorbed light?

Let's overestimate starlight and Let's overestimate starlight and neglectneglect all absorption all absorption

galaxies L density (see Part I)

2.2

88

Evolution of the Energy Density (4)Evolution of the Energy Density (4) CMB relic from a hot universe decoupling of photons→ →CMB relic from a hot universe decoupling of photons→ → Just like photons, neutrinos (Just like photons, neutrinos (νν) were initially in thermal ) were initially in thermal

equilibrium with matterequilibrium with matter At some point their cross-section diminished and they At some point their cross-section diminished and they

started free-streamingstarted free-streaming There must be a There must be a Cosmic Neutrino BackgroundCosmic Neutrino Background (CNB)! (CNB)!

Actually 3, one for each neutrino speciesActually 3, one for each neutrino species Assuming relativistic neutrinos, we get:Assuming relativistic neutrinos, we get:

Exerc!

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Evolution of the Energy Density (5)Evolution of the Energy Density (5) This calculation assumes This calculation assumes νν are always relativistic ( are always relativistic (mmνν ~ 0) ~ 0)

A given species is relativistic if particles have A given species is relativistic if particles have The mean energy of each neutrino is (see Coles & Luchini, The mean energy of each neutrino is (see Coles & Luchini,

“Cosmology (2“Cosmology (2ndnd ed.)” book) ed.)” book)

The CNB has not been directly measuredThe CNB has not been directly measured Big challenge to detect such low massBig challenge to detect such low mass

The total The total radiationradiation energy is the sum: energy is the sum:

For For zz < < zzνν → → νν become non-relativistic become non-relativistic

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Evolution of the Energy Density (6)Evolution of the Energy Density (6)

As we will see, matter contributes ~30% of the present As we will see, matter contributes ~30% of the present energy. Thus:energy. Thus:

Redshift of rad/mat equality:

Neutrinos wereradiation back then

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Evolution of the Energy Density (7)Evolution of the Energy Density (7)

Why do we use redshift all the time?Why do we use redshift all the time? It is directly measurable!It is directly measurable! aa((tt) [and thus ) [and thus zz((tt)] difficult to compute analytically)] difficult to compute analytically

From the Friedmann Equation we get:From the Friedmann Equation we get:

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Curvature-Dominated CaseCurvature-Dominated Case

Let's consider the case for which Let's consider the case for which

The Friedmann eq. Becomes:The Friedmann eq. Becomes:

Curvature must be negative (Curvature must be negative (κκ = 0 is the trivial solution) = 0 is the trivial solution) This is sometimes called a This is sometimes called a Milne universeMilne universe

Observations our universe was →Observations our universe was → nevernever close to Milne's close to Milne's

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Curvature-Dominated Case (2)Curvature-Dominated Case (2)

We can compute the proper distance today easilyWe can compute the proper distance today easily Recall light null geodesic → →Recall light null geodesic → → dsds22 = 0 = 0

So the relation between proper distance and So the relation between proper distance and zz is: is:

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Curvature-Dominated Case (3)Curvature-Dominated Case (3)

Note that for Note that for zz > > ee – 1 = 1.72, we have – 1 = 1.72, we have

The age of the Milne universe is exactly 1/The age of the Milne universe is exactly 1/HH00

How could one see light from How could one see light from zz > 1.7 then? > 1.7 then? Answer: we are computing the present distance!Answer: we are computing the present distance! The distance at emission was smaller by a factorThe distance at emission was smaller by a factor

1515

(Milne)

1616

Milne

Milne

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(Spatially) Flat Universes(Spatially) Flat Universes

Observations universe is flat, or nearly flat→Observations universe is flat, or nearly flat→ Flatness should be (at least) a good approximationFlatness should be (at least) a good approximation Assuming flatness, equations are simplerAssuming flatness, equations are simpler

Let's consider a flat universe with one component (with Let's consider a flat universe with one component (with constantconstant EoS parameter EoS parameter ww) dominating over the others) dominating over the others

Exerc!

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(Spatially) Flat Universes (2)(Spatially) Flat Universes (2)

The relation The relation zz((tt) is computed directly from ) is computed directly from aa((tt))

The proper distance is then:The proper distance is then: The proper distance is then:The proper distance is then:

It is also simple to show that for It is also simple to show that for any any ww (except – 1): (except – 1):

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Horizon DistanceHorizon Distance The most distant objects are those in our past light cone The most distant objects are those in our past light cone

for emission at for emission at tt = 0 = 0 The present proper distance for The present proper distance for tt_emission = 0 defines the _emission = 0 defines the

((particleparticle) ) horizon distancehorizon distance Objects outside the horizon cannot be observed because Objects outside the horizon cannot be observed because

their light did not have time to reach ustheir light did not have time to reach us

For For ww > – 1/3, the horizon distance is finite > – 1/3, the horizon distance is finite For For ww ≤≤ – 1/3, the horizon distance in infinite– 1/3, the horizon distance in infinite

The The whole universewhole universe is observable (& is observable (& causally connectedcausally connected)!)!

2020

Matter-Dominated CaseMatter-Dominated Case

Let's now consider the caseLet's now consider the case This is called an This is called an Einstein-de-SitterEinstein-de-Sitter universe universe Non-relativistic matter →Non-relativistic matter → ww = 0 = 0

Particular case of previous equationsParticular case of previous equations

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Radiation-Dominated CaseRadiation-Dominated Case

Let's now consider the caseLet's now consider the case This describes the early universe (pre-CMB): This describes the early universe (pre-CMB): z z >>>> 1000 1000

The mean energy of each photon is (blackbody)The mean energy of each photon is (blackbody)

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Radiation-Dominated Case (2)Radiation-Dominated Case (2) The number density The number density nn((tt) is then just:) is then just:

So both So both nn((tt) and ) and εε((tt)) formally diverge for formally diverge for tt 0→ 0→

Now for Now for ww = 1/3 we have: = 1/3 we have:

N(t) ~ 1 quantization →effects are crucial

We can only trust GR for t >> tP

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Lambda-Dominated CaseLambda-Dominated Case

Let's now consider the caseLet's now consider the case This is called a This is called a de Sitterde Sitter universe ( universe (de Sitter 1917de Sitter 1917)) This may describe the This may describe the futurefuture universe: universe: zz < – 0.5 < – 0.5

Note that the infinite future ↔Note that the infinite future ↔ zz = – 1 = – 1 Also probably an approximation for the Also probably an approximation for the inflationinflation period period

However, observations inflation is →However, observations inflation is → notnot believedbelieved to be to be caused by the cosmological constantcaused by the cosmological constant

The scale factor is no longer a power-lawThe scale factor is no longer a power-law The Hubble parameter The Hubble parameter HH((tt) becomes ) becomes constantconstant

2424

2525

Milne

MilneΛ

Λ

rad

rad

matter

matter

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Multiple-Component UniversesMultiple-Component Universes

Matter + CurvatureMatter + Curvature

Matter + Matter + ΛΛ

Matter + Curvature + Matter + Curvature + ΛΛ

Radiation + MatterRadiation + Matter

The standard model (The standard model (ΛΛCDM)CDM)

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The Hubble ParameterThe Hubble Parameter We will now deal with the full Friedmann equationWe will now deal with the full Friedmann equation

Dividing by Dividing by HH0022::

Now, we saw thatNow, we saw that So:So:

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The Hubble Parameter (2)The Hubble Parameter (2) In terms of redshift:In terms of redshift:

With the constraintWith the constraint

Multiplying by Multiplying by aa22::

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The Hubble Parameter (2)The Hubble Parameter (2)

This integral in most cases require numerical integrationThis integral in most cases require numerical integration We will have to compute it often in our courseWe will have to compute it often in our course Get familiar with numerical integration!Get familiar with numerical integration! We usually set an initial condition today an integrate to the We usually set an initial condition today an integrate to the

past (from past (from z z = 0 to = 0 to zz = = zzmaxmax))

Not all cases lead to a initial singularityNot all cases lead to a initial singularity

The comoving distance The comoving distance r r between us and a source at between us and a source at zz is: is:

Exerc!

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Matter + CurvatureMatter + Curvature This model is important as it was considered the standard This model is important as it was considered the standard

“late-time” model throughout most of the 20“late-time” model throughout most of the 20thth century century Radiation energy becomes negligible for Radiation energy becomes negligible for zz 0 we can have → HH = 0 expansion will → = 0 expansion will → stopstop at at aamaxmax and and reversereverse universe collapses→ universe collapses→ This would lead to a This would lead to a Big CrunchBig Crunch Hubble law →Hubble law → blueshiftblueshift proportional to distance proportional to distance This reversal only affects the backgroundThis reversal only affects the background

Perturbations continue to grow!Perturbations continue to grow!

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Matter + Curvature (2)Matter + Curvature (2) If If κκ ≤≤ 0, expansion never stops “Big Chill”→ 0, expansion never stops “Big Chill”→ In all cases, In all cases, a(t)a(t) can be solved analytically can be solved analytically

Parametric solutionParametric solution Note: A similar solution exists in an important case of non-Note: A similar solution exists in an important case of non-

homogenous metric (the Lemaître-Tolman-Bondi metric)homogenous metric (the Lemaître-Tolman-Bondi metric)

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Matter + Matter + ΛΛ This model is now believed to be a very good This model is now believed to be a very good

approximation of our universe for approximation of our universe for zz 0 , our universe has Λ > 0

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Matter + Matter + Λ (2)Λ (2) For For Λ > 0 and Λ < 0 analytical solution for the →Λ > 0 and Λ < 0 analytical solution for the →

Friedmann equationFriedmann equation For Λ < 0 see Ryden→For Λ < 0 see Ryden→ For Λ > 0:For Λ > 0:

Exerc!Where we defined the matter-Λ equality scale factor

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Matter + Matter + Λ (3)Λ (3) It is simple to compute the age of this universe It is simple to compute the age of this universe

Current observations tell us thatCurrent observations tell us that

Thus we would have:Thus we would have: Compare with most current measure (Planck):Compare with most current measure (Planck):

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Matter + curvature + Matter + curvature + ΛΛ This model has much richer dynamicsThis model has much richer dynamics

We can have We can have re-collapsesre-collapses,, Big-Chills Big-Chills, , Big-BouncesBig-Bounces (no Big- (no Big-Bang) and Bang) and loiteringloitering (almost static) universes (almost static) universes

No general analytical solution of Friedmann eq.No general analytical solution of Friedmann eq. It is also a good description of the universe for It is also a good description of the universe for zz

3838

Exerc!

Compute the boundary lines

between Bounce/Chill

and Chill/Crunch

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Radiation + MatterRadiation + Matter Good approximation for the early universe (Good approximation for the early universe (zz >> 2) >> 2) There is an analytical solution of Friedmann eq.There is an analytical solution of Friedmann eq.

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The The ΛΛCDM ModelCDM Model Very good description of the universe at all* timesVery good description of the universe at all* times

* - after inflation (or for * - after inflation (or for zz

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BackgroundBackground(i.e. just (i.e. just

expansion) expansion) contraints in contraints in

20112011

Suzuki et al. (1105.3470, ApJ)

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Current background contraintsCurrent background contraints

Betoule et al. (1401.4064, A&A)

4444

Current Current background background contraints contraints

w ≡

wD

E

Scolnic et al. (1710.00845, ApJ)

4545

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Chapter 6Chapter 6 Measuring Cosmological ParametersMeasuring Cosmological Parameters

The deceleration parameterThe deceleration parameter Cosmological DistancesCosmological Distances

Comoving dist.Comoving dist. Luminosity dist.Luminosity dist. Angular-diameter dist.Angular-diameter dist.

Standard CandlesStandard Candles Standard RulersStandard Rulers

Supplement BibliographySupplement Bibliography Hogg - Hogg - Distance measures in cosmology Distance measures in cosmology (astroph/9905116)(astroph/9905116)

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The deceleration parameterThe deceleration parameter It is reasonable to assume that the universe expansion is It is reasonable to assume that the universe expansion is

smooth in timesmooth in time Useful to Taylor expand Useful to Taylor expand aa((tt))

Where we defined the dimensionless decel. parameter Where we defined the dimensionless decel. parameter qq00

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The deceleration parameter (2)The deceleration parameter (2) Allan Sandage described cosmology in the 70's as a search Allan Sandage described cosmology in the 70's as a search

of two numbers: of two numbers: qq00 and and HH00 Advantages of Taylor exp. model independent quantities→Advantages of Taylor exp. model independent quantities→

qq00 and and HH00 can be related to model-dependent cosmological can be related to model-dependent cosmological

parametersparameters

Both Both qq00 and and HH00 are now well measured (errors around 10% are now well measured (errors around 10%

and 1%, respectively)and 1%, respectively) We can now go to higher order snap and jerk parameters.→We can now go to higher order snap and jerk parameters.→

See Visser 2003 (See Visser 2003 (gr-qc/0309109gr-qc/0309109)) The current trend in cosmology favors another The current trend in cosmology favors another

parametrization parametrize dark energy's →parametrization parametrize dark energy's → w(z)w(z)

https://arxiv.org/abs/gr-qc/0309109

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The deceleration parameter (3)The deceleration parameter (3) qq00 andand HH00 can be related to model-depend. cosmological param. can be related to model-depend. cosmological param.

qq0 0 →→ From the deceleration equation we get: From the deceleration equation we get:

HH0 0 →→ from the Hubble law we get: from the Hubble law we get: But how do we measure But how do we measure dd??

52

Distances in Cosmology: Distances in Cosmology: Stellar ParallaxStellar Parallax

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Distances in CosmologyDistances in Cosmology Inside the Inside the Solar SystemSolar System Laser Ranging→ Laser Ranging→

Shoot a strong laser at a planet and measure the time it Shoot a strong laser at a planet and measure the time it takes to be reflected back to ustakes to be reflected back to us

Inside the Inside the Milky WayMilky Way stellar parallax→ stellar parallax→ Requires precise astrometry.Requires precise astrometry. Maximum distance measured: 500 pc (1600 ly), by the Maximum distance measured: 500 pc (1600 ly), by the

Hipparcos satellite (1989–1993)Hipparcos satellite (1989–1993) 2013 launch of Gaia satellite (2013 – 2022) goal of → →2013 launch of Gaia satellite (2013 – 2022) goal of → →

parallaxes up to ~10 kpcparallaxes up to ~10 kpc Compare with:Compare with:

Milky Way ~15 kpc radius→Milky Way ~15 kpc radius→ Andromeda ~1 Mpc→Andromeda ~1 Mpc→

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Luminosity DistanceLuminosity Distance We can We can definedefine the luminosity distance the luminosity distance ddLL by by analogyanalogy with with

the euclidean distance given by the measured flux of a the euclidean distance given by the measured flux of a source of known intrinsic luminosity (i.e., a source of known intrinsic luminosity (i.e., a standard candlestandard candle))

In FLRW, the area of a sphere is given byIn FLRW, the area of a sphere is given by

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Luminosity Distance (2)Luminosity Distance (2) Apart from the area distortion due to curvature, Apart from the area distortion due to curvature,

expansion introduces a (1 + expansion introduces a (1 + zz))22 correction: correction: Expansion Doppler we measure → →Expansion Doppler we measure → → larger wavelengthslarger wavelengths → →

energy drops by 1 + energy drops by 1 + zz Expansion The →Expansion The → raterate of photons arriving are also smaller of photons arriving are also smaller

than the rate of photons emitted also by 1 + than the rate of photons emitted also by 1 + zz

In particular, in flat-spaces we getIn particular, in flat-spaces we get

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Angular Diameter DistanceAngular Diameter Distance For an object of known physical size For an object of known physical size ℓℓ ( (i.e.i.e. a standard a standard

ruler), the distance is related to its angular size by (for ruler), the distance is related to its angular size by (for small angles)small angles)

ℓdA

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Angular Diameter Distance (2)Angular Diameter Distance (2) Contrary to what’s written on RydenContrary to what’s written on Ryden, there is now (since , there is now (since

~2005) a very reliable standard ruler in cosmology the →~2005) a very reliable standard ruler in cosmology the →baryonic acoustic oscillation (BAO) scale (~ 150 Mpc)baryonic acoustic oscillation (BAO) scale (~ 150 Mpc) We will come back to it laterWe will come back to it later

CuriosityCuriosity: one can define the angular diameter distance in : one can define the angular diameter distance in two ways: length / angle or area / solid angletwo ways: length / angle or area / solid angle

In FLRW, both definitions coincideIn FLRW, both definitions coincide In some In some non-isotropicnon-isotropic cases, they do not! cases, they do not!

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Angular Diameter Distance (3)Angular Diameter Distance (3)

We have found that in FLRW there is a simple relation We have found that in FLRW there is a simple relation between angular diameter and luminosity distancesbetween angular diameter and luminosity distances

This a particular case of the Etherington (duality) This a particular case of the Etherington (duality) Theorem:Theorem: The above is valid in ANY metric theory (doesn't have to be The above is valid in ANY metric theory (doesn't have to be

GR, doesn't have to be FLRW)GR, doesn't have to be FLRW)

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Summary of DistancesSummary of Distances Based on HoggBased on Hogg (astroph/9905116)(astroph/9905116)

Big Big HH and small and small hh → → The Hubble Distance:The Hubble Distance:

The auxiliary function The auxiliary function E(z)E(z)::

Remember that for radial geodesics:Remember that for radial geodesics:

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Summary of Distances (2)Summary of Distances (2) So we define the So we define the line-of-sight comovingline-of-sight comoving distance as the distance as the

distance constant for objects in the Hubble flow:distance constant for objects in the Hubble flow:

AllAll other distances can be defined in terms of d other distances can be defined in terms of dCC We define the We define the transverse comovingtransverse comoving distance as the distance distance as the distance

that when multiplied by that when multiplied by δθδθ gives the comoving d gives the comoving dCC between between 2 objects at the same 2 objects at the same z z & separated by & separated by δθδθ::

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Summary of Distances (3)Summary of Distances (3) The The angular diameterangular diameter distance is given simply by: distance is given simply by:

When discussing gravitational lensing effects, one When discussing gravitational lensing effects, one naturally need to compute naturally need to compute ddAA between two objects, one at between two objects, one at zz11, the other at , the other at zz22. The . The ddAA's do 's do notnot sum! sum!

E.g.: for E.g.: for κκ < 0 (< 0 (ΩΩκκ00 > 0), we have > 0), we have Exerc!

6464

Summary of Distances (4)Summary of Distances (4) As we have shown, the As we have shown, the luminosity distanceluminosity distance is related to is related to

the angular diameter distance in a simple way:the angular diameter distance in a simple way:

The The distance modulus DMdistance modulus DM relates d relates dLL with the astronomer's with the astronomer's beloved beloved magnitudemagnitude (negative log) system (negative log) system Ancient Greeks stars visible at night were classified in 6 →Ancient Greeks stars visible at night were classified in 6 →

different apparent magnitude (different apparent magnitude (mm) categories) categories mm = 1 the brightest; → = 1 the brightest; → m m = 6 the fainter→= 6 the fainter→

The absolute magnitude The absolute magnitude MM is intrinsic. Defined as is intrinsic. Defined as mm at 10 pc. at 10 pc.

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Apparent magnitudes (Apparent magnitudes (mm) examples) examplesobject mSun – 26.7Full moon – 12.7Mars (max brightness) – 2.94Sirius (brightest star) – 1.44SN 1987A (@ Large Magellanic Cloud) 3.03Andromeda galaxy (closest galaxy) 3.44Brightest quasar (3C 273, z = 0.16) 12.9DES survey limit m (g-band) ~24.5LSST survey limit m (r-band) ~27.5Hubble Ultra Deep Field limit m ~30.5

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Summary of Distances (5)Summary of Distances (5) We can combine the previous distances to compute a We can combine the previous distances to compute a

comoving volumecomoving volume The simplest volume is a combination of 1 radial and 2 The simplest volume is a combination of 1 radial and 2

transverse separationstransverse separations For small dFor small dzz and d and dΩΩ, it is given by, it is given by

The total all-sky comoving volume in from redshift 0 to The total all-sky comoving volume in from redshift 0 to zz::

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Standard CandlesStandard Candles A plot of distance vs. A plot of distance vs. zz is called a is called a Hubble DiagramHubble Diagram To measure distances at To measure distances at zz >~ 10 >~ 10–5–5 (~0.04 Mpc) we need (~0.04 Mpc) we need

good standard candles (known intrinsic luminosity) or good standard candles (known intrinsic luminosity) or good standard rulers (known intrinsic size)good standard rulers (known intrinsic size)

There are 2 classic standard (rigorously, There are 2 classic standard (rigorously, standardiziblestandardizible) ) candles in cosmology:candles in cosmology: Cepheid variable stars (Cepheid variable stars (0 < 0 < zz < 0.01 < 0.01)) Type Ia Supernovae (Type Ia Supernovae (0 < 0 < zz < 2 < 2))

Both classes have Both classes have intrinsic variabilityintrinsic variability, but there are , but there are empirical relations that allow us to calibrate and empirical relations that allow us to calibrate and standardizestandardize them them

6868

CepheidsCepheids Cepheid variable stars are very luminous (Cepheid variable stars are very luminous (LL ~ 400 – 40000 ~ 400 – 40000

LLsunsun) stars which oscillate with period ) stars which oscillate with period PP ~ 1 – 60 days ~ 1 – 60 days Henrietta Leavitt discovered in the 1910's that there is a Henrietta Leavitt discovered in the 1910's that there is a

strong correlationstrong correlation between between PP and and LL Longer Longer PP higher ↔ higher ↔ LL By looking at the Magellanic Clouds only, she knew their By looking at the Magellanic Clouds only, she knew their

distance was ~ similardistance was ~ similar Milky Way Cepheids can be calibrated with parallaxMilky Way Cepheids can be calibrated with parallax

Measuring Measuring PP gives gives LL and and ddLL, up to some scatter, up to some scatter Scatter in distance modulus Scatter in distance modulus DMDM is ~ 0.2 mag (i.e. ~9%) is ~ 0.2 mag (i.e. ~9%) 1604.01424 measurement of 600+ Cepheids with Hubble →1604.01424 measurement of 600+ Cepheids with Hubble →

(HST) gives (HST) gives HH00 with to 2.4% precision with to 2.4% precision

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Cepheids (2)Cepheids (2) Most classical Cepheids are fundamental-mode pulsatorsMost classical Cepheids are fundamental-mode pulsators

appa

rent

mag

nitu

de

phase phase

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Cepheids (3)Cepheids (3)The The P – LP – L relation relation is calibrated with is calibrated with parallax distancesparallax distances

BlueBlue points: points: Hipparcos + Hipparcos + Hubble FCSHubble FCS

RedRed points: Hubble points: Hubble WFC3WFC3

Riess et al. (1801.01120, ApJ)

7171

Type Ia SupernovaeType Ia Supernovae Supernovae (SNe) are Supernovae (SNe) are very brightvery bright explosions of stars explosions of stars There are 2 major kinds of SNeThere are 2 major kinds of SNe

Core-collapse (massive stars which run out of H and He)Core-collapse (massive stars which run out of H and He) Collapse by mass accretion in binary systems (Collapse by mass accretion in binary systems (type Iatype Ia))

White dwarf + red giant companion (single degenerate)White dwarf + red giant companion (single degenerate) White dwarf + White dwarf (double degenerate)White dwarf + White dwarf (double degenerate) Type Ia SNe explode with a more standard energy releaseType Ia SNe explode with a more standard energy release

Chandrasekar limit on white dwarf mass: MChandrasekar limit on white dwarf mass: Mmaxmax = 1.44 M = 1.44 Msunsun Beyond this instability explosion→ →Beyond this instability explosion→ →

Besides having less intrinsic scatter, it was discovered by Besides having less intrinsic scatter, it was discovered by Phillips in '93 that there is a strong correlation between the Phillips in '93 that there is a strong correlation between the brightness and duration of a supernovaebrightness and duration of a supernovae

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SupernovaeSupernovae

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Type Ia Supernovae (2)Type Ia Supernovae (2)

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Type Ia Supernovae (3)Type Ia Supernovae (3)

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Type Ia Supernovae (2)Type Ia Supernovae (2)

After taking the stretch – luminosity correlation into After taking the stretch – luminosity correlation into account scatter in distance modulus DM ~ 0.2 – 0.3 mag→account scatter in distance modulus DM ~ 0.2 – 0.3 mag→ Current & near-future scatter only ~ 0.15 mag (i.e. ~7%)→Current & near-future scatter only ~ 0.15 mag (i.e. ~7%)→

What is the fundamental limit? 0.12 mag? 0.1 mag?What is the fundamental limit? 0.12 mag? 0.1 mag? Supernovae can be seen Supernovae can be seen very farvery far

Farthest type-Ia supernova yetFarthest type-Ia supernova yet: : zz = 1.998* = 1.998* Nearby SNe can be callibrated with Cepheids (1103.2976)Nearby SNe can be callibrated with Cepheids (1103.2976) Allows measurement of Allows measurement of ddLL to high to high zz

Allows constraints on cosmologyAllows constraints on cosmology Allows Allows 2011 Nobel Prize 2011 Nobel Prize

* Smith et al., 1712.04535

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Type Ia Supernovae (3)Type Ia Supernovae (3) Other scenearios have been proposed for Other scenearios have been proposed for type Ia SNetype Ia SNe White dwarf + White dwarf (double degenerate scenario)White dwarf + White dwarf (double degenerate scenario)

Arises from a merger, not from gas accretionArises from a merger, not from gas accretion Thus the progenitor need not be below the Chandrasekar Thus the progenitor need not be below the Chandrasekar

limitlimit Another class of SN was recently discovered: superluminous SNeAnother class of SN was recently discovered: superluminous SNe

Over 10 times brighter than type Ia Over 10 times brighter than type Ia Over 10 times more rareOver 10 times more rare Can be seen at Can be seen at zz > 3 > 3

What we are sure of:What we are sure of: SNe Ia – less intrinsic scatter + strong SNe Ia – less intrinsic scatter + strong correlation between brightness & durationcorrelation between brightness & duration

Scovacricchi, Nichol, Bacon, Sullivan, Prajs (1511.06670 – MNRAS)

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Type Ia Supernovae (4)Type Ia Supernovae (4) SNe Ia are so far the only SNe Ia are so far the only provenproven standard(izible) candles standard(izible) candles

for cosmologyfor cosmology With good measurements With good measurements →→ scatter < scatter < 0.15 mag0.15 mag in the in the

Hubble diagramHubble diagram But arguably they are subject to more systematic effects But arguably they are subject to more systematic effects

than BAO (baryon acoustic oscillations) & CMBthan BAO (baryon acoustic oscillations) & CMB Systematic errors (calibration, intervening dust, non type Ia Systematic errors (calibration, intervening dust, non type Ia

contamination, etc.) contamination, etc.) alreadyalready the dominant part (N the dominant part (NSNeSNe ~ 1000) ~ 1000)

In the next ~10 years – statistics will increase by In the next ~10 years – statistics will increase by 100x100x Huge effort to improve understanding of systematicsHuge effort to improve understanding of systematics

Howell, 1011.0441 (review of SNe)

8181

Hubble Hubble diagram diagram 1999 1999

(~50 SNe)(~50 SNe)

8282

Hubble diagram 2014 JLA catalog (740 SNe)

Hubble residual

8383

Hubble diagram log[dL(z)]

8484

ConstraintsConstraintsin 1999 in 1999 (~50 SNe)(~50 SNe)

8585

ConstraintsConstraintsin 2017 in 2017 1049 SNe1049 SNe

8686

Constraints 2014Constraints 2014

8787

The Cosmic Distance Ladder

Riess et al., 1604.01424

8888

Standard SirensStandard Sirens Gravitational waves can also be used as standard Gravitational waves can also be used as standard

candles (called standard sirens)candles (called standard sirens) Currently we can detect (with LIGO-Virgo) mergers of Currently we can detect (with LIGO-Virgo) mergers of

black-hole (black-hole (BHBH) and neutron-star () and neutron-star (NSNS) pairs) pairs LIGO-Virgo has measured 11 GW events (10 BH-BH and LIGO-Virgo has measured 11 GW events (10 BH-BH and

1 NS-NS binary merger)1 NS-NS binary merger) NS-NS (and BH-NS) mergers produce an optical NS-NS (and BH-NS) mergers produce an optical

counterpartcounterpart In the future we may detect also other GW sourcesIn the future we may detect also other GW sources

8989

Standard SirensStandard Sirens The gravitational wave detectors measure the amplitude The gravitational wave detectors measure the amplitude

and more generally the whole waveform of the GWsand more generally the whole waveform of the GWs The amplitude depends on the luminosity distanceThe amplitude depends on the luminosity distance The redshift also affects the waveform due to time-The redshift also affects the waveform due to time-

dilation, but this effect is degenerate with other GW dilation, but this effect is degenerate with other GW parameters very large errors (→parameters very large errors (→ σσzz))

If we have an optical counterpart we can also measure If we have an optical counterpart we can also measure very-well the redshift (from the host galaxy)very-well the redshift (from the host galaxy)

A pair (A pair (zz , , ddLL) = a standard candle!) = a standard candle!

9090

Current Standard SirensCurrent Standard Sirens E.g.: 4 BH-BH GWs detected by LIGOE.g.: 4 BH-BH GWs detected by LIGO

9191

σσddLL ~30–50% (0.7–1 mag) BH-BH & ~25% (0.5 mag) NS-NS ~30–50% (0.7–1 mag) BH-BH & ~25% (0.5 mag) NS-NS

Correlated with e.g. orbital inclination angle & chirp mass Correlated with e.g. orbital inclination angle & chirp mass ΜΜ

Current Standard SirensCurrent Standard Sirens

LIGO-Virgo coll., 1811.12907

9292

E.g.: HE.g.: H00 from 1 Siren (GW170817) from 1 Siren (GW170817)

9393

– – End of Part II –End of Part II –

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