6th Week: The Early Universe and Big Bang Nucleosynthesis

Cosmological Principle

According to the standard model of the cosmological principle, which only holds true on cosmological scales on approximately greater than 300 to 500 Mpc;

$k>0\Rightarrow$ the universe is viewed as closed $\Rightarrow$ end result Big Crunch

$k=0\Rightarrow$ the universe is viewed as flat $\Rightarrow$ end result forever expansion

$k<0\Rightarrow$ the universe is viewed as open $\Rightarrow$ end result Big Chill

Robertson-Walker Cosmology Now we come to the

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.