Cosmological solutions of the Einstein-Friedmann equations ...

Cosmology
A) Empty Worlds, vacuum energy at most: ρ = p = 0 , Λ = κ ρvac
In spite of the fact that such models are unrealistic, they give some insight into the
geometrical and kinematic possibilities in cosmological model building. In this
limiting case we have the following basic equations:
or
˙S 2
c 2 = Λ
3 S 2 − k ;
¨S
c 2 = Λ
3 S
Λ = −3 H2 (t)
c 2 q(t) ; K(t) = − H2 (t)
c 2 (q(t) + 1) .
c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 441