Consensus Inflation 163SB 3B 1 A 1A 210 –^4310 –^3510171030101081
t[s]B 4B 2Figure 7.3Evolution of the scale푅of the Universe since Planck time in (A) Friedmann models
and (B) inflationary expansion. During the epoch B 1 the Universe expands exponentially, and
during B 2 the inflation ends by reheating the Universe. After the graceful exit from inflation
the Universe is radiation dominated along B 3 ,justasinA 1 , following a Friedmann expansion.
The sections B 4 and A 2 are matter-dominated epochs.
domain walls and the coalescence of bubbles. In some models knots or topological
defects then remained in the form of monopoles of the order of one per bubble. Thus
the inflationary model also solves the monopole problem by blowing up the size of
the region required by one monopole. There remains no inconsistency then with the
present observed lack of monopoles.
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.
Although Guth’s classical model of cosmic inflation may seem to solve all the prob-
lems of the hot Big Bang scenario in principle, it still fails because of difficulties with
the nucleation rate. If the probability of bubble formation is large, the bubbles collide
and make the Universe inhomogeneous to a much higher degree than observed. If
the probability of bubble formation is small, then they never collide and there is no
reheating in the Universe, so each bubble remains empty. Thus there is no graceful
exit from this inflationary scenario.