Smooth Hybrid Inflation with Low Reheat Temperature and Observable Gravity Waves in $SU(5) \times U(1)_{\chi}$ Super-GUT

TL;DR

This paper presents a supersymmetric $SU(5) imes U(1)_{ ext{chi}}$ model that achieves smooth hybrid inflation with low reheat temperature, observable gravity waves, and solutions to monopole and proton decay problems, aligning with current cosmological and particle physics constraints.

Contribution

It introduces a novel supersymmetric GUT framework with specific Kähler potential modifications to realize successful inflation, dark matter candidates, and proton decay predictions.

Findings

Scalar spectral index $n_s$ within Planck bounds

Tensor-to-scalar ratio $r$ up to 0.056

Reheat temperature compatible with leptogenesis

Abstract

We realize smooth hybrid inflation in the framework of supersymmetric $SU(5) \times U(1)_{\chi}\subset SO(10)$ model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of $SU(5)$. The breaking of $U(1)_{\chi}$ symmetry leaves a residual discrete $Z_2$ symmetry, that serves as the MSSM matter parity, realizing the possibility of the lightest supersymmetric particle as a cold dark matter candidate. The $d = 5$ proton lifetime for the decay $p \rightarrow K^+ \bar{\nu}$, mediated by color-triplet Higgsinos is found to satisfy current experimental bounds if split-high scale SUSY scenario is employed. We show that with minimal K\"ahler potential, the soft supersymmetry breaking terms play a vital r\^ole in bringing the scalar spectral index $n_s$ within the Planck's latest bounds. In a minimal K\"ahler potential setup, small values of tensor-to-scalar ratio $r \lesssim 3.5 \times 10^{-7}$ are obtained, whereas the gravitino mass turns out to be in the range that favors PeV scale SUSY but is not sufficiently high to avoid the $d = 5$ proton decay. A non-minimal K\"ahler potential including higher-order corrections is required to realize successful inflation with central value of scalar spectral index $n_s = 0.9655$, large tensor modes $r \lesssim 0.056$ and a low reheat temperature $(3\times 10^{6} \lesssim T_r \lesssim 6.5 \times 10^7 )$ GeV consistent with leptogenesis and baryogenesis.