$U(1)_{B-L}$ Dark Matter Constrains Smooth (SUSY) Hybrid Inflation

Abstract

We propose a unified framework that connects inflationary dynamics with dark matter production within a supersymmetric $U(1)_{B-L}$ extension of the Standard Model. The setup is based on smooth hybrid inflation embedded in supergravity, with a non-minimal Kahler potential ensuring control of higher-order corrections. The model involves three scalar fields: the inflaton $σ$, an auxiliary field $ζ$ responsible for ending inflation, and a singlet mediator $η$ that links the inflationary and dark sectors. Dark matter is realized as an inert scalar stabilized by a $\mathbb{Z}_2$ symmetry and produced non-thermally via reheating dynamics. We show that reproducing the observed dark matter relic abundance imposes strong constraints on the inflationary sector, significantly reducing the allowed parameter space. As a result, the scalar spectral index is tightly constrained to $n_s \simeq 0.972 - 0.974$, consistent with current observational bounds. While the inflaton-dark matter coupling has a negligible effect on the background evolution, it induces observable modifications in the tensor-to-scalar ratio and the spectrum of primordial gravitational waves. This establishes a direct link between dark matter physics and inflationary observables.