with the restriction w 6 = − 1. With the proper normalization, the scale factor
in a spatially flat, single-component universe is
a(t) = (t/t 0 ) 2/(3+3w) , (5.41)
where the age of the universe, t 0 , is linked to the present energy density by
the relation
t 0 =
1
1 + w à c 2
6πGε 0 !
1/2
. (5.42)
The Hubble constant in such a universe is
H 0 ≡ µ ˙a
a ¶ t=t 0
=
2
3(1 + w)
t −1
0