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

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 $-2\times 10^{-6}\lesssim d{n}_s/d\ln k\lesssim -5\times 10^{-11}$ 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.

12 pages, 7 figures

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