$\mu$-hybrid Inflation, Gravitino Dark Matter and Stochastic Gravitational Wave Background from Cosmic Strings

TL;DR

This paper develops a supersymmetric $$-hybrid inflation model with $U(1)_{B-L}$ symmetry, linking gravitino dark matter, leptogenesis, and cosmic string-generated gravitational waves, consistent with Planck and NANOGrav observations.

Contribution

It introduces a novel supersymmetric inflation model incorporating $U(1)_{B-L}$, connecting dark matter, leptogenesis, and gravitational wave predictions within observational bounds.

Findings

Reheat temperature range $2 imes 10^{7}$ to $5 imes 10^{9}$ GeV.

Tensor-to-scalar ratio $r$ between $2 imes 10^{-18}$ and $4 imes 10^{-13}$.

String tension parameter $G ext{μ}_ ext{cs}$ within $10^{-9}$ to $10^{-6}$, matching NANOGrav data.

Abstract

We present a successful realization of supersymmetric $\mu$-hybrid inflation model based on a gauged $U(1)_{B-L}$ extension of the minimal supersymmetric standard model, with the soft supersymmetry breaking terms are playing an important role. Successful non-thermal leptogenesis with gravitino dark matter yields a reheat temperature in the range $2 \times 10^{7} \lesssim T_R \lesssim 5 \times 10^{9}$ GeV. This corresponds to the predictions $2 \times 10^{-18} \lesssim r\lesssim 4 \times 10^{-13}$ for the tensor to scalar ratio, and $-2 \times 10^{-6} \lesssim dn_s/d\ln k \lesssim -5 \times 10^{-11}$ for the running of the scalar spectral index. The $B-L$ breaking scale is estimated as $ 6 \times 10^{14}\lesssim M/ \text{GeV}\lesssim 10^{16}$, calculated at the central value of the scalar spectral index, $n_s =0.9655$, reported by Planck 2018. Finally, in a grand unified theory setup the dimensionless string tension parameter associated with the metastable strings is in the range $ 10^{-9} \lesssim G\mu_\text{cs} \lesssim 10^{-6}$ corresponding to a stochastic gravitational wave background lying within the 2$\sigma$ bound of the recent NANOGrav 12.5-yr data.