Astro 321 Set 1: FRW Cosmology - Wayne Hu's Tutorials

Multicomponent Universe
• Friedmann equation gives Hubble parameter evolution in a
H 2 (a) = H 2 0
Ωie − d ln a 3(1+wi)
• In fact we can always define a critical equation of state
wc = pc
wiρi − ρK/3
=
ρc
i ρi + ρK
• Critical energy density obeys energy conservation
ρc(a) = ρc(a = 1)e − d ln a 3(1+wc(a))
• And the Hubble parameter evolves as
H 2 (a) = H 2 0e − d ln a 3(1+wc(a))