Cosmology and Dark Matter I: Einstein & the Big Bang by Jerry Sellwood

The Expanding Universe Hubble discovered that galaxies move away at a rate proportional to their distance v = H 0 d where H 0 is known as “Hubble’s constant” HST key project measured H 0 = 72  8 km/s/kpc

Our position is not special Every other observer would see the same The entire universe is expanding and there is no center All galaxies were closer together in the past –at time  1 / H 0 distances were zero

Origin of the redshift Galaxies are not really moving –the space between them is expanding Photons from distant galaxies were emitted when the universe was smaller and have been stretched by the subsequent expansion of the universe Distances in an expanding universe scale everywhere with time by a scale factor a(t) –We choose a(t 0 ) = 1 –and the expansion rate today is da/dt = H 0 a If the redshift is z, then a = 1 / ( 1 + z )

General Relativity Principle of equivalence –A gravitational field and an accelerating reference frame are indistinguishable Implies light must curve in a gravitational field But light always travels by the shortest path So mass causes space to become curved A uniformly dense universe must be uniformly curved

Is the universe uniform? We will assume the universe is –(a) homogeneous –(b) isotropic At least on very large scales Supporting evidence: –Radio galaxies Baleisis et al (1998) The distribution of radio sources brighter than 70mJy from combined surveys of the N & S Aitoff projection (equal area) in RA & dec

3-D distribution SDSS redshift survey –Every dot is a galaxy in a slice (incomplete) –fewer distant galaxies because they are fainter Clustering hierarchy reveals big density variations Averages over very large volumes seem constant

Curved Spacetime A uniform & isotropic universe must be one of 3 possible curved spacetimes –positively curved (4-sphere) –negatively curved (4-saddle) –flat

Friedmann’s equation In a uniform universe, Einstein’s equations can be reduced to a single differential equation where –  is the energy density (matter + radiation), –  is a possible “cosmological constant”, –R is the radius of curvature, and  = 1 for an open universe  = –1 for a closed universe  = 0 for a flat universe Note that the geometry cannot change

Newton & Einstein Both men worried: –if gravity is always attractive –why hasn’t the universe collected into one glob? Einstein added the repulsive  term to his field equations in order to allow a static universe Expanding universe discovered later –declared his cosmological constant “my greatest blunder”

Critical density Neglect the  term for the time being If H 2 = 8  G  /3, the equation requires  = 0 – a flat universe Thus if    crit = 3H 2 / 8  G –space is negatively curved (  =  1) –the universe is open and expands forever whereas if    crit –space is positively curved (  =  1) –the universe is closed and will eventually recollapse

Equations of state The energy density decreases as the universe expands. Two cases: –non-relativistic matter:   a -3 = (1+z) 3 –relativistic matter + radiation:   a -4 = (1+z) 4 Also curvature term varies as (1+z) 2 So at high redshift, the energy term is always the largest

The Hot Big Bang The universe expands adiabatically Photons lose energy because of the redshift t 0 approx 13.7  0.2 Gyr  4.3  s

Nucleosynthesis I There was a very slight excess of baryons over anti-baryons Annihilations left a vast excess of photons over particles After 0.5s, lose thermal equilibrium between neutrons and protons Neutrons start to decay

Nucleosynthesis II A few seconds later, photons are no longer able to dissociate deuterium In next three minutes almost all available neutrons are absorbed into 4 He nuclei Reactions stop as the temperature and density continue to drop

Nucleosynthesis III Final abundances depend on: –the photon to baryon ratio –the expansion rate, which places a limit on the number of relativistic species (e.g. neutrinos)

Tests of BBN Hard to find unpolluted primordial material that is accessible spectroscopically Best work is by primordial 2 H abundance by Tytler – in absorption lines in QSO spectra

Baryon fraction 2 H, 4 He, 3 He & 7 Li abundances must all be consistent with one value of the ratio of photons to baryons Know the number of CMB photons Therefore baryon fraction is  4% of the closure density today

Matter-radiation equality Next milestone Very little happens Expansion rate changes

Formation of the CMB For 300,000 years, the intense radiation keeps hydrogen ionized H + + e   H +  Constant scattering of photons –maintains thermal equilibrium with matter –makes the universe opaque But as photons are redshifted, atoms are quite suddenly able to survive The universe quickly becomes neutral and transparent

Cosmic Microwave Background Universe is filled with the relic radiation from the big bang It is redshifted now to T=2.725 K Spectrum is a near perfect black body with a peak in the microwave

Re-ionization Diffuse gas in the universe did not stay neutral for long First stars and/or quasars emitted enough UV radiation to ionize all the diffuse gas Density is far too low by that time for the ionized gas to be opaque