Prof Subir Sarkar

Abstract:

We study the cosmology of the Supersymmetric Standard Model augmented by a gauge singlet to solve the $\mu$-problem and describe the evolution of the domain walls which are created during electroweak symmetry breaking due to the discrete $Z_{3}$ symmetry in this model. The usual assumption, that non-renormalizable terms induced by gravity (which explicitly break this symmetry) may cause the walls to collapse on a cosmologically safe timescale, is reconsidered. Such terms are constrained by considerations of primordial nucleosynthesis, and also by the fact that by not respecting the $Z_{3}$ symmetry they induce divergences which destabilise the hierarchy and reintroduce the $\mu$--problem. We find that, even when the K\"ahler potential is `non-minimal' (i.e. when the hidden sector couples directly to the visible) the model is either ruled out cosmologically or suffers from a naturalness problem.

Abstract:

We reconsider the problems of cosmological inflation in effective supergravity theories. A singlet field in a hidden sector is demonstrated to yield an acceptable inflationary potential, without fine tuning. In the simplest such model, the requirement of generating the microwave background anisotropy measured by COBE fixes the inflationary scale to be about $10^{14}$ GeV, implying a reheat temperature of order $10^{5}$ GeV. This is low enough to solve the gravitino problem but high enough to allow baryogenesis after inflation. Such consistency requires that the generation of gravitational waves be negligible and that the spectrum of scalar density perturbations depart significantly from scale-invariance, thus improving the fit to large-scale structure in an universe dominated by cold dark matter. We also consider the problems associated with gravitino production through inflaton decay and with other weakly coupled fields such as the moduli encountered in (compactified) string theories.