Solving the $\eta$-Problem in Hybrid Inflation with Heisenberg Symmetry and Stabilized Modulus

TL;DR

This paper introduces a model using Heisenberg symmetry to resolve the $ ext{eta}$-problem in supersymmetric hybrid inflation, stabilizing the modulus without fine-tuning, and compatible with string theory and particle physics.

Contribution

It presents a new class of inflation models that stabilize the modulus and solve the $ ext{eta}$-problem using Heisenberg symmetry, with a specific example based on sneutrino hybrid inflation.

Findings

Spectral index within WMAP range

Tensor-to-scalar ratio very small

Modulus stabilized without fine-tuning

Abstract

We propose a class of models in which the $\eta$-problem of supersymmetric hybrid inflation is resolved using a Heisenberg symmetry, where the associated modulus field is stabilized and made heavy with the help of the large vacuum energy during inflation without any fine-tuning. The proposed class of models is well motivated both from string theory considerations, since it includes the commonly encountered case of no-scale supergravity Kaehler potential, and from the perspective of particle physics since a natural candidate for the inflaton in this class of models is the right-handed sneutrino which is massless during the inflationary epoch, and subsequently acquires a large mass at the end of inflation. We study a specific example motivated by sneutrino hybrid inflation with no-scale supergravity in some detail, and show that the spectral index may lie within the latest WMAP range, while the tensor-to-scalar ratio is very small.