260 Inflation I: homogeneous limit
escapes from the maximum not via tunneling, but due to the quantum fluctuations.
It then slowly rolls towards the global minimum where the energy is released
homogeneously in the whole space. Originally the pre-inflationary state of the
universe was taken to be thermal so that the symmetry was restored due to thermal
corrections. This was a justification for the initial conditions of the scalar field.
Later it was realized that the thermal initial state of the universe is quite unlikely,
and so now the original motivation for the initial conditions in the new inflationary
model seems to be false. Instead, the universe might be in a “self-reproducing”
regime (for more details see Section 8.5).
Chaotic inflationis the name given to the broadest possible class of potentials
satisfying the slow-roll conditions (Figure 5.7(c)). We have considered it in detail
in the previous sections. The namechaoticis related to the possibility of having
almost arbitrary initial conditions for the scalar field. To be precise, this field must
initially be larger than the Planckian value but it is otherwise arbitrary. Indeed, it
could have varied from one spatial region to another and, as a result, the universe
would have a very complicated global structure. It could be very inhomogeneous
on scales much larger than the present horizon and extremely homogeneous on
“small” scales corresponding to the observable domain. We will see in Section 8.5
that in the case of chaotic inflation, quantum fluctuations lead to a self-reproducing
universe.
Since chaotic inflation encompasses so many potentials, one might think it worth-
while to consider special cases, for example, an exponential potential. For an ex-
ponential potential, if the slow-roll conditions are satisfied once, they are always
satisfied. Therefore, it describes (power-law) inflation without a graceful exit. To
arrange a graceful exit we have to “damage” the potential. For two or more scalar
fields the number of options increases. Thus it is not helpful here to go into the
details of the different models.
In the absence of the underlying fundamental particle theory, one is free to
play with the potentials and invent more new scenarios. In this sense the situation
has changed since the time the importance of inflation was first realized. In fact,
in the 1980s many people considered inflation a useful application of the Grand
Unified Theory that was believed to be known. Besides solving the initial condi-
tions problem, inflation also explained why we do not have an overabundance of the
monopoles that are an inevitable consequence of a Grand Unified Theory. Either
inflation ejects all previously created monopoles, leaving less than one monopole
per present horizon volume, or the monopoles are never produced. The same ar-
gument applies to the heavy stable particles that could be overproduced in the
state of thermal equilibrium at high temperatures. Many authors consider the solu-
tion of the monopole and heavy particle problems to be as important as a solution