New smooth hybrid inflation

Abstract

We consider the extension of the supersymmetric Pati-Salam model which solves the b-quark mass problem of supersymmetric grand unified models with exact Yukawa unification and universal boundary conditions and leads to the so-called new shifted hybrid inflationary scenario. We show that this model can also lead to a new version of smooth hybrid inflation based only on renormalizable interactions provided that a particular parameter of its superpotential is somewhat small. The potential possesses valleys of minima with classical inclination, which can be used as inflationary paths. The model is consistent with the fitting of the three-year Wilkinson microwave anisotropy probe data by the standard power-law cosmological model with cold dark matter and a cosmological constant. In particular, the spectral index turns out to be adequately small so that it is compatible with the data. Moreover, the Pati-Salam gauge group is broken to the standard model gauge group during inflation and, thus, no monopoles are formed at the end of inflation. Supergravity corrections based on a non-minimal Kaehler potential with a convenient choice of a sign keep the spectral index comfortably within the allowed range without generating maxima and minima of the potential on the inflationary path. So, unnatural restrictions on the initial conditions for inflation can be avoided.