Solving the η-problem in hybrid inflation with Heisenberg symmetry and stabilized modulus

Abstract

We propose a class of models in which the η-problem ofsupersymmetric hybrid inflation is resolved using a Heisenbergsymmetry, where the associated modulus field is stabilized andmade heavy with the help of the large vacuum energy duringinflation without any fine-tuning. The proposed class of models iswell motivated both from string theory considerations, since itincludes the commonly encountered case of no-scale supergravityKähler potential, and from the perspective of particle physicssince a natural candidate for the inflaton in this class of modelsis the right-handed sneutrino which is massless during theinflationary epoch, and subsequently acquires a largemass at the end of inflation. We study a specific example motivated by sneutrino hybrid inflation with no-scale supergravityin some detail, and show that the spectral index may lie withinthe latest WMAP range, while the tensor-to-scalar ratio is verysmall.