A $U(1)_R$ inspired inflation model in no-scale Supergravity

TL;DR

This paper explores a no-scale supergravity inflation model with $U(1)_R$ symmetry, proposing a superpotential deformation to achieve a potential similar to Starobinsky inflation, and discusses parameter correlations for successful inflation.

Contribution

It introduces a novel deformation of the superpotential in no-scale supergravity with $U(1)_R$ symmetry to realize inflation similar to Starobinsky's model.

Findings

The deformed superpotential yields a suitable inflationary potential.

Successful inflation requires specific parameter correlations.

The model predicts spectral index and tensor-to-scalar ratio consistent with observations.

Abstract

We consider a cosmological inflation scenario based on a no-scale supergravity sector with $U(1)_R$ symmetry. It is shown that a tree level $U(1)_R$ symmetric superpotential alone does not lead to a slowly rolling scalar potential. A deformation of this tree level superpotential by including an explicit $R$ symmetry breaking term beyond the renomalizable level is proposed. The resulting potential is found to be similar (but not exactly the same) to the one in Starobinsky inflation model. We emphasize that for successful inflation, with the scalar spectral index $n_s \sim 0.96$ and the tensor-to-scalar ratio $r < 0.08$, a correlation between the mass parameters in the superpotential and the vacuum expectation value of the modulus field $T$ in the K\"ahler potential must be adopted.