170 Cosmic Inflation
ordinary matter and radiation are created by oscillations in the potential well, or by
entropy generation during a second slow-roll phase of an equally arbitrary dark energy
field. Clearly, any viable alternative to single-field inflation must also be able to solve
the problems in Section 7.1, and it should not contain more arbitrary elements than
does single-field inflation—multiple scalar fields have more freedom but also more
arbitrariness.
In the radiation-dominated Universe, the source of energy of photons and other
particles is a phase transition or a particle decay or an annihilation reaction, many
of these sources producing monoenergetic particles. Thus the energy spectrum pro-
duced at the source is very nonuniform and nonrandom, containing sharp spectral
lines ‘ordered’ by the type of reaction. Such a spectrum corresponds to low entropy.
Subsequent scattering collisions will redistribute the energy more randomly and ulti-
mately degrade it to high-entropy heat. Thermal equilibrium is the state of maximum
uniformity and highest entropy. The very fact that thermal equilibrium is achieved at
some time tells us that the Universe must have originated in a state of low entropy.
In the transition from radiation domination to matter domination no entropy is
lost. We have seen the crucial effect of photon reheating due to entropy conservation
in the decoupling of the electrons. As the Universe expands and the wavelengths of the
CMB photons grow, the available energy is continuously converted into lower-grade
heat, thus increasing entropy. This thermodynamic argument defines apreferred direc-
tion of time.
When the cooling matter starts to cluster and contract under gravity, a new phase
starts. We have seen that the Friedmann–Lemaitre equations dictate instability, the
lumpiness of matter increases with the Universe developing from an ordered, homo-
geneous state towards chaos. It may seem that contracting gas clouds represent higher
uniformity than matter clustered into stars and galaxies. If the only form of energy
were thermal, this would indeed be so. It would then be highly improbable to find a gas
cloud squeezed into a small volume if nothing hinders it from filling a large volume.
However, the attractive nature of gravity seemingly reverses this logic: the cloud gains
enormously in entropy by contracting. Thus the preferred direction of time as defined
by the direction of increasing entropy is unchanged during the matter-dominated era.
The same trend continues in the evolution of stars. Young suns burn their fuel
through a chain of fusion reactions in which energetic photons are liberated and heav-
ier nuclei are produced. As the photons diffuse in the stellar matter, they ultimately
convert their energy into a large number of low-energy photons and heat, thereby
increasing entropy. Old suns may be extended low-density, high-entropy red giants or
white dwarfs, without enveloping matter which loses mass by various processes. In
the process of supernova explosion entropy grows enormously.
Consider the contracting phase of an oscillating universe. After the time푡maxgiven
by Equation (5.52) the expansion turns into contraction, and the density of matter
grows. If the age of the Universe is short enough that it contains black holes which
have not evaporated, they will start to coalesce at an increasing rate. Thus entropy
continues to increase, so that the preferred direction of time is unchanged. Shortly
before the Big Crunch, when the horizon has shrunk to linear size퐿p, all matter has
probably been swallowed by one enormously massive black hole.