168 Cosmic Inflation
continuously the volume of space grows by a factor
e(^3 −ln 2)Ht, (7.56)whereas in the parts of space-time where휙does not decrease the volume grows by
the factor
1
2
e^3 Ht. (7.57)
Since the Hubble parameter is proportional to휙, most of the physical volume must
come from bubbles in which휙is maximal:
휙≃푀P^2 ∕푚휙. (7.58)But there must also be an exponential number of bubbles in which휙is smaller. Those
bubbles are the possible progenitors of universes of our kind. In them,휙attains finally
the value corresponding to the true minimum푉(휙 0 ), and a Friedmann–Lemaitre-type
evolution takes over. Elsewhere the inflatoric growth continues forever. Thus we hap-
pen to live in a universe which is a minuscule part of a steady-state eternally inflating
meta-universe which has no end, and therefore it also has no beginning. There is sim-
ply no need to turn inflation on in the first place, and the singularity at time zero has
dropped out from the theory.
During inflation, each bubble is generating new space-time to expand into, as
required by general relativity, rather than expanding into pre-existing space-time. In
these de Sitter space-times the bubble wall appears to an observer as a surrounding
black hole. Two such expanding bubbles are causally disconnected, so they can nei-
ther collide nor coalesce. Thus the mechanism of vacuum-energy release and transfer
of heat to the particles created in the phase transition is not by bubble collisions as in
the classical model. Instead, the rapid oscillations of the inflaton field휙decayawayby
particle production as the Universe settles in the true minimum. The potential energy
then thermalizes and the Universe reheats to some temperature of the order of푇GUT.
In this reheating, any baryon–anti-baryon asymmetry produced during the GUT
phase transition mechanism is washed out, that is why some other phase transition
must be sought to explain the baryon–anti-baryon asymmetry. Thus the existence of
baryons is an indication that particle physics indeed has to go beyond the ‘minimal
standard model’.
7.4 Predictions
One consequence of the repulsive scalar field is that any two particles appear to repel
each other. This is the Hubble expansion, which is a consequence of inflation. In non-
inflationary theories the Hubble expansion is merely taken for granted.
Inflationary models predict that the density of the Universe should today be very
nearly critical,
훺 0 = 1. (7.59)This prediction is verified to within 0.3 %. Consequently, we should not only observe
that there is too little luminous matter to explain the dynamical behavior of the