Cosmic background fluctuations 87the heat that flows during a reversible change. If no heat flows during a reversible
change, then entropy must be conserved, and the expansion will beadiabatic.
This can only be an approximation, since there will exist irreversible microscopic
processes. In practice, however, it will be shown later that the effects of these
processes are overwhelmed by the entropy of thermal background radiation in the
universe. It will therefore be an excellent approximation to treat the universe as
if the matter content were a simple dissipationless fluid undergoing a reversible
expansion. This means that, for a ratio of specific heats,wegettheusual
adiabatic behaviour
T∝R−^3 (−^1 ).
For radiation, = 4 /3 and we get justT ∝ 1 /R. A simple model for the
energy content of the universe is to distinguish pressureless ‘dust-like’ matter (in
the sense thatpρc^2 ) from relativistic ‘radiation-like’ matter (photons plus
neutrinos). If these are assumed not to interact, then the energy densities scale as
ρm∝R−^3 ρr∝R−^4The universe must therefore have beenradiation-dominatedat some time in
the past, where the densities of matter and radiation cross over. To anticipate,
we know that the current radiation density corresponds to thermal radiation with
T 2 .73 K. In addition to this CMB, we also expect a background in neutrinos.
This arises in the same way as the CMB: both photons and neutrinos are in thermal
equilibrium at high redshift, but eventually fall out of equilibrium as the universe
expands and reaction timescales lengthen. Subsequently, the number density of
frozen-out background particles scales asn ∝a−^3 , exactly as expected for a
thermal background withT∝ 1 /a. The background appears to stay in thermal
equilibrium even though it has frozen out. If the neutrinos are massless and
therefore relativistic, they contribute an energy density comparable to that of the
photons (to be exact, a factor 0.68 times the photon density—see p 280 of Peacock
(1999)). If there are no other contributions to the energy density from relativistic
particles, then the total effective radiation density isrh^2 4. 2 × 10 −^5 and the
redshift ofmatter–radiation equalityis
1 +zeq=23 900h^2 (T/ 2 .73 K)−^4.The time of this change in the global equation of state is one of the key
epochs in determining the appearance of the present-day universe. By a
coincidence, this epoch is close to another important event in cosmological
history: recombination. Once the temperature falls below 104 K, ionized
material can form neutral hydrogen. Observational astronomy is only possible
from this point on, since Thomson scattering from electrons in ionized material
prevents photon propagation. In practice, this limits the maximum redshift of
observational interest to about 1000; unlessis very low or vacuum energy is
important, a matter-dominated model is therefore a good approximation to reality.