The measured present-day density parameters are matter and radiation (photons plus…

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Astrophysics & Cosmology · Einstein's field equations

The Geometry of Gravity, Ch FRW cosmology as an exact solution

Problem

The measured present-day density parameters are matter

\Omega_{\rm m} = 0.311

and radiation (photons plus neutrinos)

\Omega_{\rm r} = 8.4\times10^{-5}

, with

a(t_0) = 1

. Each component dilutes as

\rho_i \propto a^{-3(1+w_i)}

, with

w_{\rm m} = 0

and

w_{\rm r} = 1/3

. ((a)) Estimate the scale factor

a_{\rm eq}

at which the matter and radiation energy densities were equal. ((b)) Estimate the corresponding redshift

z_{\rm eq} = 1/a_{\rm eq} - 1