Cosmological solutions of the Einstein-Friedmann equations ...

Cosmology
The general solution is
S (t) = a ct + b ; Λ = 0 , a 2 = −k ,
S (t) = 1
2
a e αct + b e −αct ; Λ 0 , α 2 = Λ
3
Because of time reversal symmetry or anti-symmetry:
when b 0: b = ±a with a > 0.
Cases:
(a) Λ = 0 , k = 0: S = S 0 = constant ; H = 0 , q = 0 .
; Λ
3
(b) Λ = 0 , k = −1: S = ct ; H = 1/t , q = 0 ; z = t0/t1 − 1 ,
Milne’s Universe
(c) Λ > 0 , k = 1: S = a cosh
ct
a .
ab = k = (1, 0, −1) .
c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 442