New inflation
20 I
magnetic monopole contribution to the predicted density of the universe today
derived from the size of the ratio of the monopole number density to the entropy
density at the time of the grand unified phase transition at which the monopoles
were produced or, equivalently, from the size of the ratio of the number of
monopoles to the entropy. The problem can be solved if a great deal of entropy is
generated by inflation.
During supercooling, the entropy does not change. However. the nonadiabatic reheating results in increased entropy. The entropy density prior to
supercooling is of order T;. If the reheating temperature T R "" Tc, the entropy
density is still of this order after reheating. However, because the volume of
any region has been inflated by the inflation of R3. the entropy in that region
has increased by a factor of e 3H l!J.t, where III is the duration of the period of
exponential expansion. If there is sufficient inflation to solve the flatness problem
(about 64 e-folds of inflation), then the entropy increases by a factor of 2.4 x 10 83 .
In section 3.10, we found that for the case of a supersymmetric grand-unified
phase transition. QMh2 was 18-19 orders of magnitude greater than the predicted
upper bound for Qh2 (and a few orders of magnitude more in the case of a firstorder phase transition). Since the entropy generation resulting from inflation
reduces QMh2 by 83 orders of magnitude, the relic monopole density today is
insignificant. A similar discussion applies to other particle relics.
For all its successes, old inflation has a fatal flaw. It is not possible to make
a 'graceful exit' [2] from the period of inflationary expansion in a supercooling
de Sitter universe to a reheated FRW universe. The problem arises because the
phase transition is completed in the way described in section 2.9 by the formation
of bubbles of the true vacuum inside the false vacuum. In the first instance, the
vacuum energy of the de Sitter phase emerges as energy in the bubble walls. For
the universe to thermalize, it is necessary for the bubble walls to undergo many
collisions with other bubble walls. The trouble is that, on the one hand, sufficient
inflation requires the nucleation rate for the true vacuum to be sufficiently low
to allow a long period of supercooling. On the other hand, if bubbles of true
vacuum are to form sufficiently rapidly for the bubbles to overlap and collide in
an expanding universe, then this same nucleation rate needs to be sufficiently high.
It turns out that these two requirements cannot be reconciled. More precisely, it
is found that for nucleation rates low enough for sufficient inflation the universe
always consists of clusters of bubbles of true vacuum with a few bubbles in each
cluster surrounded by false vacuum.
7.4 New inflation
It is possible to retain the successes of old inflation while avoiding the graceful
exit problem in an alternative formulation of cosmological inflation referred to as
'new' inflation [3-5] or 'slow-roll' inflation. The graceful exit problem derived
from the slow rate of bubble formation at a first-order phase transition when
20 I
magnetic monopole contribution to the predicted density of the universe today
derived from the size of the ratio of the monopole number density to the entropy
density at the time of the grand unified phase transition at which the monopoles
were produced or, equivalently, from the size of the ratio of the number of
monopoles to the entropy. The problem can be solved if a great deal of entropy is
generated by inflation.
During supercooling, the entropy does not change. However. the nonadiabatic reheating results in increased entropy. The entropy density prior to
supercooling is of order T;. If the reheating temperature T R "" Tc, the entropy
density is still of this order after reheating. However, because the volume of
any region has been inflated by the inflation of R3. the entropy in that region
has increased by a factor of e 3H l!J.t, where III is the duration of the period of
exponential expansion. If there is sufficient inflation to solve the flatness problem
(about 64 e-folds of inflation), then the entropy increases by a factor of 2.4 x 10 83 .
In section 3.10, we found that for the case of a supersymmetric grand-unified
phase transition. QMh2 was 18-19 orders of magnitude greater than the predicted
upper bound for Qh2 (and a few orders of magnitude more in the case of a firstorder phase transition). Since the entropy generation resulting from inflation
reduces QMh2 by 83 orders of magnitude, the relic monopole density today is
insignificant. A similar discussion applies to other particle relics.
For all its successes, old inflation has a fatal flaw. It is not possible to make
a 'graceful exit' [2] from the period of inflationary expansion in a supercooling
de Sitter universe to a reheated FRW universe. The problem arises because the
phase transition is completed in the way described in section 2.9 by the formation
of bubbles of the true vacuum inside the false vacuum. In the first instance, the
vacuum energy of the de Sitter phase emerges as energy in the bubble walls. For
the universe to thermalize, it is necessary for the bubble walls to undergo many
collisions with other bubble walls. The trouble is that, on the one hand, sufficient
inflation requires the nucleation rate for the true vacuum to be sufficiently low
to allow a long period of supercooling. On the other hand, if bubbles of true
vacuum are to form sufficiently rapidly for the bubbles to overlap and collide in
an expanding universe, then this same nucleation rate needs to be sufficiently high.
It turns out that these two requirements cannot be reconciled. More precisely, it
is found that for nucleation rates low enough for sufficient inflation the universe
always consists of clusters of bubbles of true vacuum with a few bubbles in each
cluster surrounded by false vacuum.
7.4 New inflation
It is possible to retain the successes of old inflation while avoiding the graceful
exit problem in an alternative formulation of cosmological inflation referred to as
'new' inflation [3-5] or 'slow-roll' inflation. The graceful exit problem derived
from the slow rate of bubble formation at a first-order phase transition when