Introduction to Cosmology

Consensus Inflation 161

Inhomogeneities of the energy density increase as the Universe develops from an
ordered, homogeneous low-entropy state towards a high-entropy chaos characterized
by lower-grade heat. Thus the increase in entropy defines apreferred direction of time,
thermal equilibrium being 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.
As the Universe cools through the critical temperature푇GUT, bubbles of the cool
phase start to appear and begin to grow. If the rate of bubble nucleation is initially
small the Universe supercools in the hot phase, very much like a supercooled liquid
which has a state of lowest potential energy as a solid.
The lowest curve in Figure 6.1 and the curve in Figure 7.2 illustrates the final situ-
ation when the true minimum has stabilized at휙 0 (denoted휑 0 in the figures), and the
potential energy of this true vacuum is lower than in the originalfalse vacuum:

푉(휙 0 ,푇cool)<푉( 0 ,푇hot).

As the potential steepens, the inflaton field begins to oscillate coherently about its
vacuum state at the minimum of the potential. When the phase transition from the
supercooled hot phase to the cool phase finally occurs at푇coolthe latent heat stored
as vacuum energy is liberated,reheatingthe Universe and filling it with radiation and
kinetic energy of ultrarelativistic massive scalar particles with positive pressure. At the
same time other GUT fields present massify in the process of spontaneous symmetry
breaking, suddenly filling the Universe with particles of the reheating temperature푇R.
Precisely how this occurs is not known, but many scenarios have been proposed.
The liberated energy heats the Universe enormously, of the order of

⟨푉 0 ⟩≃(푘푇R)^4 , (7.38)

from an ambient temperature

푇cool≪푇R

to푇R,whichisatthe푇GUTscale. Only at this time can one talk about a hot Big Bang.

φend reheating

φ

δφ

V(φ)

φCMB

Δφ

φ

Figure 7.2Potential energy for a real scalar field휙.