70 The hot universe
black holes. We will see later that the data on light element abundances and CMB
fluctuations clearly indicate that the baryonic component contributes only a small
percentage of the critical energy density( (^) b 0. 04 ). The number of photons per
baryon is of order 10^9.
Dark matter and dark energy The CMB fluctuations imply that at present
the total energy density is equal to the critical density. This means that the largest
fraction of the energy density of the universe is dark and nonbaryonic. It is not quite
clear what constitutes this dark component. Combining the data on CMB, large scale
structure, gravitational lensing and high-redshift supernovae it appears that the dark
component is a mixture of two or more constituents. More precisely, it is composed
ofcold dark matteranddark energy. The cold dark matter has zero pressure and can
cluster, contributing to gravitational instability. Various (supersymmetric) particle
theories provide us with natural candidates for the cold dark matter, among which
weakly interacting massive particlesare most favored at present. The nonbaryonic
cold dark matter contributes only about 25% of the critical density. The remaining
70% of the missing density comes in the form of nonclustered dark energy with
negative pressure. It may be either a cosmological constant (p=−ε) or a scalar
field (quintessence) withp=wε,wherewis less than− 1 /3 today.
Primordial neutrinosThese are an inevitable remnant of a hot universe. If the
three known neutrino species were massless, their temperature today would be
Tν 1 .9 K and they would contribute 0.68 times the radiation density (see Section
3.4.2). Atmospheric neutrino oscillation experiments suggest that the neutrinos
have small masses. Even so, it appears that they cannot constitute more than 1% of
the critical density.
The universe was hotter and denser in the past. The energy densities of radiation,
cold matter and dark energy scale with redshiftzas
εγ=εγ 0 (1+z)^4 ,εm=εcr 0
m(1+z)^3 ,εQ=εcr 0
Q(1+z)3(1+w), (3.1)
respectively. Hereε 0 cr= 3 H 02 / 8 πGis the critical density today, (^) mis the total
contribution of baryons and cold dark matter to the current cosmological parameter
and (^) Qis the contribution of dark energy. When we go back in time the dark energy
density grows the least quickly; its impact on the dynamics of the universe becomes
less than that of cold matter at redshift (see Figure 3.1)
zQ=( (^) Q/
m)−^1 /^3 w− 1. (3.2)
This occurs close to the present time, atzQ= 0 .33 to 1. 33 ,for− 1 ≤w<− 1 / 3 ,
(^) m≈ 0 .3 and (^) Q≈ 0. 7.
Problem 3.1Find the value ofzat which the accelerated expansion begins.