Subcritical regime of hybrid inflation with modular $A_4$ symmetry

TL;DR

This paper explores a supergravity model with modular $A_4$ symmetry linking neutrino mixing and inflation, predicting an inverted hierarchy, a specific Majorana phase, and constraining the Majorana mass scale.

Contribution

It introduces a novel supergravity model with modular $A_4$ symmetry that connects neutrino properties with inflationary dynamics, providing new predictions and bounds.

Findings

Only inverted neutrino mass hierarchy is allowed.

Majorana phase predicted around ±(120–180)°.

Upper bound of ~10^{10} GeV on Majorana mass scale.

Abstract

We consider a supergravity model that has the modular $A_4$ symmetry and discuss the interplay between the neutrino mixing and inflation. The model contains right-handed neutrinos that have the Majorana masses and additional Yukawa couplings to the waterfall field. In the model an active neutrino is massless and we find that only the inverted hierarchy is allowed and the Majorana phase is predicted to be around $\pm (120\text{--}180)^\circ$ from the observed neutrino mixing data. In the early universe, one of right-handed sneutrinos plays the role of the inflaton field. Focusing on the subcritical regime of the hybrid inflation that is consistent with the cosmic microwave background data, we analyze the dynamics of the scalar sector and derive an upper bound $\mathcal{O}(10^{10})~{\rm GeV}$ on the scale of the Majorana mass.