Eternal inflation and collapse theories

Abstract: 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.