**2.2. Are defects inflated away?**

It is important to realize the relevance that the Kibble's mechanism
has for cosmology; nearly every sensible grand unified theory (with
its own symmetry breaking pattern) predicts the existence of defects.
We know that an early era of inflation helps in getting rid of the
unwanted relics. One could well wonder if the very same Higgs field
responsible for breaking the symmetry would not be the same one
responsible for driving an era of inflation, thereby diluting the
density of the relic defects.
This would get rid not only of (the unwanted) monopoles and
domain walls but also of any other (cosmologically appealing) defect.
Let us follow
[Brandenberger, 1993]
and sketch why this actually does not occur.
Take first the symmetry breaking potential of Eq. (1.2)
at zero temperature and add to it
a harmless -independent term
3 *m*^{4} /
(2). This will
not affect the dynamics at all. Then we are led to

(5) |

with = ( 6
*m*^{2} /
)^{1/2}
the symmetry breaking energy scale,
and where for the present heuristic digression we just took a real
Higgs field. Consider now the equation of motion for
,

(6) |

for <<
very near the
false vacuum of the effective Mexican hat potential and
where, for simplicity, the expansion of the universe and
possible interactions of
with other fields were neglected.
The typical time scale of the solution is t *m*^{-1}.
For an inflationary epoch to be effective we need
t >> *H*^{-1}, *i.e.*, a sufficiently large
number of e-folds
of slow-rolling solution. Note, however, that after some
e-folds of exponential expansion the curvature term in
the Friedmann equation becomes subdominant and we have
*H*^{2}
8*G* *V*(0) /
3
(2*m*^{2} /
3 )( /
*m*_{P})^{2}.
So, unless
> *m*_{P}, which seems unlikely for a GUT phase
transition, we are led to
<< *H*^{-1} and therefore
the amount of inflation is not enough for getting rid of
the defects generated during the transition by hiding them
well beyond our present horizon.

Recently, there has been a large amount of work in getting defects,
particularly cosmic strings, after post-inflationary preheating.
Reaching the latest stages of the inflationary phase, the inflaton
field oscillates about the minimum of its potential. In doing so,
parametric resonance may transfer a huge amount of energy to other
fields leading to cosmologically interesting nonthermal phase
transitions. Just like thermal fluctuations can restore broken
symmetries, here also, these large fluctuations may lead to the whole
process of defect formation again. Numerical simulations employing
potentials similar to that of Eq. (1.5) have shown that
strings indeed arise for values
~
10^{16} GeV
[Tkachev et al., 1998,
Kasuya & Kawasaki,
1998].
Hence, preheating after inflation helps in generating cosmic defects.