Cosmology Universe – everything we can detect Questions: Infinite or finite? Is there an edge, a...

Cosmology• Universe – everything we can detectQuestions:• Infinite or finite?• Is there an edge, a center?• How old is it?Olber’s Paradox (actually discussed much earlier, by

Digges, Kepler, Halley):Why is the sky dark at night?

Assumptions: static and infinite Universe Universe is uniformly filled with stars

Then, in any direction, line-of-sight will intersect a star the sky should be as bright as the surface of a star?

(of course, L is proportional to 1/distance2, but number of stars increases as distance2)

Olbers suggested light blocked by intervening clouds of matter can’t work, because clouds would heat up and radiate (sky would still be bright)

were our initial assumptions wrong?

A solution suggested by E.A. Poe (yes, him!)• What if the Universe were created at some time

in the past?• With a long enough “look-back” time, there

would be no stars….Basic Assumptions of Cosmology:1. Homogeneity – matter uniformly distributed in

space2. Isotropy – Universe looks the same in all

directions3. Universality – physical laws we know on Earth

apply everywhere

1) & 2) are known as the “Cosmological Principle”Note: the assumptions only apply on the largest

scales – there is ample evidence for local inhomogeneity, anisotropy (e.g. galaxies)

Also: evolutionary changes not considered

Expansion of the Universe:• Hubble detected redshifts of galaxies• Velocity proportional to distance (like raisins in

a rising loaf of bread)But… are redshifts really due to motion?

General Relativity: • Expansion of Universe is really an expansion of

space-time itself• Photons are “stretched” when traveling through

expanding space-time hence, shifted to longer wavelengths

Curvature of Space-Time:• General Rel. – mass curves space-time• We experience the curvature as a gravitational

field• The total amount of mass defines the geometry of

the Universe

How can we comprehend this?• Imagine an ant walking on an orange; e.g., a

two-dimensional Universe – finite, but unbounded (i.e., edge-less)

3 different curvatures (geometries) possible:1. Zero – “flat” Universe – in this case, the area of

circle = π r2 – same for larger radii2. Positive – “closed Universe – as radius of a

circle increases, the area increases at < π r2

3. Negative – “open Universe – as radius of a circle increases, the area increases at > π r2

Now, in 3-dimensions, we deal with volumes of spheres instead of areas of circles.

• In “flat” Universe: volume = 4/3 π r3

How can we determine the curvature?• Count galaxies – if the number increases

proportional to r3, Universe is “flat” – if the number increases more quickly with radius, the Universe is “open”, if more slowly, it’s closed

Also: both open and flat cases – Universe is infinite; closed case – Universe is finite, but edgeless (like the orange)

Big Bang Theory• Universe began in a high temperature, high

density state not at a single point, the Big Bang filled entire volume of the Universe

• We can look back to the era of the Big Bang; radiation from that time is highly redshifted (to IR, radio)

• Gamov (1948) – predicted that early Big Bang was hot, emitted blackbody radiation in present era, we’d see a redshifted blackbody spectrum

• Penzias & Wilson (early 1960’s ; won Nobel Prize, 1978) – radio measurements of the sky; found “noise”

• “Noise” turned out to be Cosmic Microwave Background Radiation

But…was it a black-body?• Cosmic Background Explorer (COBE) 1989;

confirmed it was B-body (T = 2.7 K, in agreement with predictions) – z ~ 1000

• Originally from gas clouds of T ~ 3000K• Almost perfectly isotropic – some blueshift in

direction of the Milky Way’s motion towards Virgo Cluster

A timeline:

• At t = 0; matter in state where physics not well understood

• At t = 10 millionths of a second –T > 1012K, density ~ 5 x 1013 gm/cc (same as an atomic nucleus)

At this point, Universe was entirely in the form of radiation (but, E = M c2)

• And γ-rays decay particles, antiparticles• As Universe expands – wavelengths increase,

Energy decreases cools off• At t = 0.0001 sec, T < 1012 K, γ-ray decay can no

longer produce protons, neutrons (although electron/positron pairs can be produced until t = 4 seconds)

• Cooling/expanding continue until atomic nuclei form

• At t = 2 minutes: p + n deuterium

• At t = 3 minutes: deuterium helium

But, nothing heavier (no stable atomic nuclei with atomic weights 5 – 8)

• At t = 30 minutes – nuclear reactions mstop; 25% of mass in He nuclei; rest is in H nuclei (i.e. protons) – same as oldest stars

• Up until t ~ 106 years – dominated by radiation; gas ionized

Photons can’t travel far (interact with electrons) – matter and radiation are coupled

• At t = 106 years – cool enough to form atoms; gas becomes transparent to radiation (Recombination) – T ~ 3000 K – this is the point where the CMB radiation originates

Matter now dominates

Future of the Universe:• Question of density hence, geometry• “critical density” – 4 x 10-30 g/cc; results in

a “flat” Universe• If density < critical density open• If density > critical density closed• If the Universe is open or flat will

expand forever; gravity may slow expansion, but will never stop it

• If Universe is closed: expansion stops, followed by contraction and collapse to high density state (“Big Crunch”)

• Oscillating Universe? Probably not.

How do we measure the density?

• Galaxy counts (but, hard to really determine the mass); and what about dwarf galaxies?

• Best estimate ~ 5 x 10-31 g/cc• But > 90% may be in form of Dark Matter;

from study of lensing, mass 10 times greater than estimated from luminosity – halos 10 to 20 times larger than visible parts of galaxies so, 10 x more mass

Deuterium:• Amount depends on density of early Universe• Can be destroyed, but no longer created• In gas near Quasars, 25 D per every 106 H atom –

tells us that the Universe was not so dense that more D He

Taking all into account, maybe 5% of mass required for a flat Universe

Regarding Dark Matter:

• Exotic non-interacting particles (WIMPs)

• Neutrinos (not enough of them); also, can’t account for galaxy formation (too “hot”)

• MACHOs – massive compact halo objects; should act as gravitational lenses – a few detected, but not enough

Quantum Universe

• “flatness” – why a flat Universe (note, we are within a factor of 10 of critical density)

• “horizon problem” – isotropy of CMB (same to 1 part in 1000)

At time of recombination, gas was transparent to radiation – but… not enough time for signals to travel from one region to another

“Inflationary Universe”• Sudden expansion when Universe very young• 4 fundamental forces: Gravity, Electromagnetism,

Strong, Weak – Unification: Electromagnetism and Weak force same at high energies

• “Grand Unification Theories” – in early Universe, all 4 forces unified

• At t = 10-35 sec, fundamental forces separated: huge amounts of energy released, Universe inflated by factor of 1020 to 1030

Solves problems – inflation forces curvature to zero (“Flatness”) and temperatures equalized before inflation (“Horizon”)

Quantum Mechanics predicts spontaneous creation of matter/anti-matter -- maybe how Universe appeared in the first place

Age of Universe:

Distance/velocity = time, but v = H x d;

So, T = (1 / H) x 1012 years

• Doesn’t account for gravity

• If H = 80, Universe is younger than oldest globular clusters!

• Best current values – age of globulars ~ 11 x 109 years, H ~ 70; Universe is 13.5 x 109 years, so OK, but a concern……

Cosmological Constant:• Einstein (1916) – didn’t know Universe was

expanding --- need force to keep it from collapsing; Λ – “Cosmological Constant”

• Hubble saw redshifted galaxies, so Λ = 0, everything Ok, right?

• By looking at Type Ia Supernovae in very distant galaxies, get distances – expected to see expansion slow down But… saw just the opposite!!

• Thus, Λ is not = 0; what is going on? Energy from Q.M. processes in empty space? Maybe….

• Anyhow, if Λ > 0, Universe could be older than

1 / H (so, no worries about stars older than the Universe)

• Also: critical mass – normal matter 5%; dark matter 25%; rest in form of empty space (E = Mc2)

Structure of Universe:• Superclusters groups in filaments/walls• CMB is uniformHow did the structure form out of the hot gas in the

Big Bang?Also – must have occurred early (Quasars at look-

back time 93% of the age of the Universe)• Cold dark matter – galaxies• Hot dark matter – filaments• But, what are the galaxy “seeds” – QM

fluctuations, magnified by Inflation – consistent with small CMB fluctuations detected by COBE