Gauge Non-Singlet Inflation in SUSY GUTs

We explore the novel possibility that the inflaton responsible for cosmological inflation is a gauge non-singlet in supersymmetric (SUSY) Grand Unified Theories (GUTs). For definiteness we consider SUSY hybrid inflation where we show that the scalar components of gauge non-singlet superfields, together with fields in conjugate representations, may form a D-flat direction suitable for inflation. We apply these ideas to SUSY models with an Abelian gauge group, a Pati-Salam gauge group and finally Grand Unified Theories based on SO(10) where the scalar components of the matter superfields in the $\sixteen$s may combine with a single $\bar {sixteen}$ to form the inflaton, with the right-handed sneutrino direction providing a possible viable trajectory for inflation. Assuming sneutrino inflation, we calculate the one-loop Coleman-Weinberg corrections and the two-loop corrections from gauge interactions giving rise to the "gauge \eta-problem" and show that both corrections do not spoil inflation, and the monopole problem can be resolved. The usual \eta-problem arising from supergravity may also be resolved using a Heisenberg symmetry.