Shift Symmetry and Inflation in Supergravity

We consider models of inflation in supergravity with a shift symmetry. We focus on models with one moduli and one inflaton field. The presence of this symmetry guarantees the existence of a flat direction for the inflaton field. Mildly breaking the shift symmetry using a superpotential which depends not only on the moduli but also on the inflaton field allows one to lift the inflaton flat direction. Along the inflaton direction, the η-problem is alleviated. Combining the KKLT mechanism for moduli stabilization and a shift symmetry breaking superpotential of the chaotic inflation type, we find models reminiscent of “mutated hybrid inflation” where the inflationary trajectory is curved in the moduli–inflaton plane. We analyze the phenomenology of these models and stress their differences with both chaotic and hybrid inflation.