Cosmological solutions of the Einstein-Friedmann equations ...

Cosmology
Form of energy equation of state q0 q0(k = 0)
a) vacuum energy: pΛ = −ρΛ q0 = −ΩΛ q0 = −1,
b) non-relativistic matter: pmat = 0 q0 = 1
2 Ωmat q0 = 1
2 ,
c) relativistic matter, radiation: prad = ρrad/3 q0 = Ωrad q0 = 1,
the different forms of matter contribute with different signs and weights to q0.
Whatever the mix of energies the total energy density
ρ(t) = ρ0,crit
⎧
⎪⎨
⎪⎩ ΩΛ + Ω0,mat
3 S 0
S (t)
+ Ω0,rad
for t → 0 is dominated in any case by the radiation part:
ρtot ρ0,crit Ω0,rad
4 S 0
S (t)
⎫
4
S 0 ⎪⎬
S (t) ⎪⎭
c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 474
,
i.e.