Cosmological solutions of the Einstein-Friedmann equations ...

Cosmology
The critical energy density and the flatness problem
In general we have some mixture of vacuum energy, relativistic and non-relativistic
matter. We have seen that the Einstein-de Sitter universe with k=0 plays a special
role. In the present matter dominated era ρEdS plays the boundary case between
expansion forever or recontraction. We therefore define
ρ0,crit = ρEdS = 3H2 0
8πGN = 1.878 × 10−29 h 2 gr/cm 3 ,
where H0 is the present Hubble constant, and h its value in units of 100 km s −1
Mpc −1 , and express the energy density in units of ρ0,crit. Thus the present density
ρ0 is represented by
and
Ω0 = ρ0/ρ0,crit
c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 470