NONSTANDARD PRIMORDIAL FLUCTUATIONS FROM A POLYNOMIAL INFLATION POTENTIAL

We examine in detail the properties of inflation determined from the most general renormalizable potential for a single real scalar field φ: V(φ) = Aφ4/4 + Bφ3/3 + Cφ2/2 + V0. We find sets of parameters that can strongly break scale invariance, with a valley in the usual Zel'dovich spectrum. Such a valley can lead to earlier galaxy formation and more large scale structure in the Universe than in the usual scale-invariant cold dark matter scenario. We also find that the parameters of the potential can be many orders of magnitude larger than what would be allowed without the inclusion of the cubic term, which can lead to high reheat temperatures Treh ∼ 1015 GeV. We have mapped out all regions of parameter space and have identified those regions that produce interesting behavior, as well as the entire region that leads to an acceptable inflationary scenario with small enough fluctuations. We further explore the possibility of generating interesting non-gaussian adiabatic density fluctuations from this potential, and find that it is unlikely for general single scalar field potentials that do not contain false vacua in the path of the inflation, as significant non-gaussian behavior implies too large a fluctuation amplitude. © 1990.