Cosmology: Building the Universe.
The term has several different meanings. We are interested in physical cosmology the study of the origin and development of the physical universe, and all the
structure within it.
Important questions:
• How was the large-scale structure generated?
• How was mattter created (specifically the baryon/photon ratio)?
• Will the universe expand forever? (Why is the density so close to the critical
value?)
• Is the universe infinite?
- Are there other “universes?”
- Can it matter to us?
Constraints from Observational Cosmology
1) Expansion of the galaxies (the Hubble flow).
2) The structure of the universal, thermal background radiation.
3) (Hierarchical) Large-scale structure:
superclusters ––> clusters ––> groups ––> galaxies ––> star clusters…
4) Relative abundances of the light elements.
5) Distribution of dark matter (and dark energy: what’s the matter in the
universe?).
6) Ages of star clusters.
7) The process of galaxy formation and evolution.
Observational constraints 1: The age of the universe.
• The oldest stars: in globular clusters and the MW halo - 12-14 billion yrs.
• The Hubble constant (expansion age of the universe): τ ∝ 1/Ho ≈ 13.5 Gyr.
The two independent estimates give the same age.
––> the universe began about 13.5 Gyr ago with all matter (and space-time)
concentrated at a single point. (This is the conclusion of the singularity theorems
of general relativistic cosmology.)
The expansion began with a Big Bang! A quantum fluctation?
Will the universe expand forever?
• Cosmological equations imply that the universe is dynamic. It must expand or
collapse (generic solutions).
• Is there sufficient mass in the universe for gravity to overcome the inertia of
expansion? (Is there more than inertia to overcome, like accelerated expansion?)
• That depends on the mean density relative to the critical density (assuming no
extra acceleration):
ρcrit ≈ 1.1 x 10-26 h752 kg/m3
• If Ω = ρ/ρcrit > 1, then - the universe is closed and will recollapse in the future.
• If Ω < 1, then - the universe is open, and expansion continues forever.
We need to measure Ω (and the extra acceleration) to determine the fate of the
universe.
Measuring Ωo.
• Method 1: Add up the mass in the universe.
- First add up the baryon mass in galaxies, and get Ωo ≤ 0.03.
- Add in dark matter in galaxies, groups, and clusters and get Ωo ≈ 1/3.
(Open universe?)
- Not really, add in the mass-energy of the dark energy and get Ωo ≈ 1.
• Method 2: Measure the Hubble flow of distant (early) galaxies.
- Expansion was different at early times.
- Higher density (closed) universe ––> much faster expansion.
- Rate of change (curvature) of Hubble law ––> constraint on Ωo, Λ.
• Method 3: Careful, statistical study of cosmic background radiation constrains
combinations of cosmological parameters.
Note: strong philosophical bias for Ωo ≤ 1.0. Maybe becoming justified by
observation.
Observational Constraints 2: The Microwave Background (CMB).
Prior to t ≈ 106 yrs: - The universe was opaque. There was more mass-energy in
photons than matter (radiation dominated). T ≥ 3000 K, so all H ionized.
At 106 yrs: Matter dominates, H recombines, and the universe becomes
transparent.
The most distant time we can hope to “see” is recombination (redshift ≈ 1500).
Presently the universe is fill with 3 K background radiation, left over from the heat
of the Big Bang & recombination.
1950s: background radiation “predicted” by Gamow.
1965: discovered by Penzias and Willson.
1990: Cosmic Background Explorer maps spectrum
- precisely a Planck spectrum.
- distributed almost uniformly.
COBE
WMAP
Observational Constraints 3: Big Bang Nucleosynthesis
• Before the first few minutes the universe was so hot that nuclei broke apart as
quickly as they could fuse.
• At t ≈ 3 min. It is hot enough to make deuterium, He, and a few other light
elements, but cool enough for them to hold together.
• Later… further expansion and cooling halts fusion.
Detailed calculations show that the Big Bang produce: ~ 75% H, 25% He, ≤ 0.1%
everything else. The fact that old stars have a similar composition supports
Big Bang models.
Nucleosynthesis Epoch (t ≈ 102-3 s)
Need sufficient energy in thermal motions to nearly overcome Coulomb
repulsion between two protons at typical nuclear separations. But relativistic
particles don’t fuse.
Protons and neutrons decouple at temperature of - T ≈ (mpc2)/k ≈ 1013 K.
For some time thereafter ρ, T are high enough to maintain thermal equilibrium in
the p, n abundances. E.g., in reactions like:
νe + n <––> e- + p,
And
n <––> p + e- + νe.
He is formed in the reaction series:
p + n <––> D + γ
D + D <––> 3He + n <––> 3H + p
3H
+ D <––> 4He + n.
(low density means 2-body reactions only)
Problem: D is easily broken. Must have T ≤ 3 x 109 K to build sufficient
abundance.
However, at that time the density is too low to maintain equilibrium.
Relaxation time ≈ expansion time.
I.e., some important reaction times have become too long.
Nonetheless, most neutrons are incorporated into He nuclei before freezeout,
where, fusion times > expansion time.