cosmology and dark matter i: einstein & the big bang by jerry sellwood
TRANSCRIPT
The Expanding Universe
• Hubble discovered that galaxies move away at a rate proportional to their distance
v = H0 d
where H0 is known as “Hubble’s constant”
• HST key project measured
H0 = 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 / H0 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(t0) = 1
– and the expansion rate today is da/dt = H0 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 H2 = 8G/3, the equation requires = 0
– a flat universe
• Thus if crit = 3H2 / 8G– 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
• t0 approx 13.70.2 Gyr 4.31018s
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 4He 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 2H abundance by Tytler – in absorption lines in QSO spectra
Baryon fraction
• 2H, 4He, 3He & 7Li 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
Formation of the CMB• For 300,000 years, the intense radiation
keeps hydrogen ionizedH+ + 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