  The eternal inflation problem continues to be considered one of standard's
cosmology most serious shortcomings. This arises when one considers the effects
of "quantum fluctuations" (QF) on the zero mode of inflaton field during a
Hubble time in the inflationary epoch. In the slow-roll regime it is quite
clear that such QF could dwarf the classical rolling down of the inflaton, and
with overwhelming probability this prevents inflation from ever ending. When
one recognizes that QF can not be taken as synonymous of stochastic
fluctuations, but rather intrinsic levels of indefiniteness in the quantities,
one concludes that the eternal inflation problem simply does not exist.
However, the same argument would serve to invalidate the account for the
generation of the primordial seeds of cosmic structure. In order to do address
that issue, one must explain the breaking of homogeneity and isotropy of the
early inflationary epoch. The so called spontaneous collapse theories offer an
additional element namely the stochastic and spontaneous state reduction
characteristic of those proposals possesses the basic features to break those
symmetries. In fact, a version of the CSL theory adapted to the cosmological
context has been shown to offer a satisfactory account for the origin the seeds
of cosmic structure with an adequate power spectrum, and will serve as the
basis of our analysis. However, once such stochastic collapse is introduced
into the theoretical framework the eternal inflation problem has the potential
reappear. In this manuscript we explore those issues in detail and discuss an
avenue that seems to allow for a satisfactory account for the generation of the
primordial inhomogeneities and anisotropies while freeing the theory from the
eternal inflation problem.
