6th Week: The Early Universe and Big Bang Nucleosynthesis

Robertson-Walker Cosmology

From the large-scale distribution of galaxies and the near-uniformity of the CMB temperature, we have good evidence that the universe is nearly homogeneous and isotropic. Under this assumption, the space-time metric can be written in the FRW form

where r, θ, φ are comoving spatial coordinates and t is time, and where the expansion is described by the cosmic scale factor, a(t) (by convention, a = 1 today). The quantity k is the curvature of three-dimensional space: k = 0 corresponds to a spatially flat, Euclidean universe, k > 0 to positive curvature (three-sphere), and k < 0 to negative curvature (saddle). The wavelengths λ of photons moving through the universe scale with a(t), and the redshift of light emitted from a distant source at time tem, 1 + z = λobs/λem = 1/a(tem), directly reveals the relative size of the universe at that time. This means that time intervals are related to redshift intervals by dt = −dz/H(z)(1 + z), where H ≡ a˙/a is the Hubble parameter, and the overdot denotes a time derivative. The present value of the Hubble parameter is conventionally expressed as H0 = 100 h km/sec/Mpc, where h ≈ 0.7 is the dimensionless Hubble parameter. Here and below, a subscript 0 on a parameter denotes its value at the present epoch.

Density Evolution

Evolution of radiation, matter, and dark energy densities with redshift.For dark energy, the band represents w = −1 ± 0.2.