Physical Foundations of Cosmology

3.1 The composition of the universe 71

zeq zQ 0 z

(^) m
(^) γ
(^) Q
Fig. 3.1.
The radiation energy density grows faster than the density of cold matter and
eventually becomes dominant at redshift
zeq=
εcr 0
m
εγ 0
− 1  2. 26 × (^104) mh^275 , (3.3)
where
h 75 ≡

H 0

75 km s−^1 Mpc−^1

.

Thus, we can distinguish three dynamically different stages in the expansion
history:

 the radiation-dominated epochatz>zeq∼ 104 ,where the universe is dominated by

ultra-relativistic matter withp=ε/3 and scale factor increases asa∝t^1 /^2 ;


 the matter-dominated epochatzeq>z>zQ,where the pressureless components deter-

mine the expansion rate anda∝t^2 /^3 ;


 the dark-energy-dominated epochatz<zQ,where the component with negative pres-

sure,p=wε,leads to an accelerated expansion anda∝t^2 /^3 (^1 +w).

Note that the dark energy cannot begin to dominate too early because a substantial
period of matter domination is needed for structure formation. In fact, it becomes
relevant exactly at the present time. This astounding cosmic coincidence is one of
the greatest mysteries of contemporary cosmology.

Problem 3.2How do ultra-relativistic neutrinos influence an estimate for the red-
shift at which the ultra-relativistic matter begins to dominate?