Cosmic inflation and $(g-2)_\mu$ in minimal gauged $L_\mu-L_\tau$ model

TL;DR

This paper explores a minimal gauged $L___ au$ model that addresses the muon g-2 anomaly and proposes the $U(1)_{L___ au}$ Higgs as an inflaton, linking particle physics with early universe cosmology.

Contribution

It introduces a cosmological scenario where the $U(1)_{L___ au}$ Higgs acts as the inflaton, connecting muon g-2 resolution with inflationary constraints.

Findings

Allowed reheating temperature window is very narrow.

Severe restrictions on the $(n_s-r)$ inflationary parameter plane.

Consistent cosmological history constrains the model parameters.

Abstract

The minimal $U(1)_{L_\mu-L_\tau}$ gauge symmetry extended Standard Model (SM) is a well motivated framework that resolves the discrepancy between the theoretical prediction and experimental observation of muon anomalous magnetic moment. We envisage the possibility of identifying the beyond Standard Model Higgs of $U(1)_{L_\mu-L_\tau}$ sector, non-minimally coupled to gravity, as the inflaton in the early universe, while being consistent with the $(g-2)_\mu$ data. Although the structure seems to be trivial, we observe that taking into consideration of a complete cosmological history starting from inflation through the reheating phase to late-time epoch along with existing constraints on $U(1)_{L_\mu-L_\tau}$ model parameters leave us a small window of allowed reheating temperature. This further results into restriction of $(n_s-r)$ plane which is far severe than the one in a generic non-minimal quartic inflationary set up.