Non-Zel’dovich Fluctuations from Inflation

Abstract

I review the recent work of the Santa Cruz group on the generation of non-Zel’dovich (including non-Gaussian) fluctuations in chaotic inflation. With a single inflaton having the most general quartic polynomial potential, most of the space of the parameters of the potential corresponds to fluctuations with an approximately Zel’dovich spectrum. To the extent that significant deviations from the Zel’dovich spectrum arise, the spectrum characteristically has a dip at a particular scale; in this case the usual upper limit on the quartic coefficient is relaxed and the reheat temperature is correspondingly increased. In the context of the cold dark matter model, such a dip spectrum may help explain both increased large scale structure and earlier galaxy formation. If we consider a general inflaton potential, it is possible to invert the slow-roll equations of motion and find the potential corresponding to almost any desired fluctuation spectrum. In models with multiple inflatons such as double inflation, de Sitter fluctuations in the second inflaton generated during the inflationary period controlled by the first inflaton make it impossible to preset the value of the second inflaton, and thus to get structure in the fluctuation spectrum on a cosmologically interesting scale. Regarding non-Gaussian fluctuations (nGf), we distinguish between local and non-local nGf. With a single inflaton, the inflationary nGf are negligible if the fluctuation amplitude lies below the upper limit from nonobservation of cosmic background radiation fluctuations. Several nonstandard possibilities arise in the generation of non-local nGf such as cosmic strings and texture, with the corresponding scalar fields either free or coupled to the inflaton or to curvature. In particular, such cosmic strings typically correspond to a strongly Type I superconductor, a case that should be investigated further.