# Higgs mechanism and cosmological constant in $N=1$ supergravity with inflaton in a vector multiplet

## TL;DR

This paper reformulates supergravity models of inflation with a vector multiplet as supersymmetric gauge theories, analyzing their scalar potential and stability of de Sitter vacua including a positive cosmological constant.

## Contribution

It introduces a new formulation of supergravity inflation models using supersymmetric U(1) gauge theories with explicit analysis of vacuum stability.

## Key findings

- Scalar potential computed and de Sitter vacuum found stable
- Reformulation as supersymmetric U(1) gauge theories
- Inclusion of positive cosmological constant (dark energy)

## Abstract

The $N=1$ supergravity models of cosmological inflation with inflaton belonging to a massive vector multiplet and spontaneous SUSY breaking after inflation are reformulated as the supersymmetric $U(1)$ gauge theories of a massless vector superfield interacting with the Higgs and Polonyi chiral superfields, all coupled to supergravity. The $U(1)$ gauge sector is identified with the $U(1)$ gauge fields of the super-GUT coupled to supergravity, whose gauge group has a $U(1)$ factor. A positive cosmological constant (dark energy) is included. The scalar potential is calculated, and its de Sitter vacuum solution is found to be stable.