Cosmic inflation and (g-2)μin minimal gauged Lμ-Lτmodel

The minimalU(1)L mu-L tau gauge symmetry extended Standard Model (SM) is awell motivated framework that resolves the discrepancy between the theoretical prediction andexperimental observation of muon anomalous magnetic moment. We envisage the possibilityof identifying the beyond Standard Model Higgs ofU(1)L mu-L tau sector, non-minimally coupledto 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 considerationof a complete cosmological history starting from inflation through the reheating phase tolate-time epoch along with existing constraints onU(1)L mu-L tau model parameters leave us asmall window of allowed reheating temperature. This further results into restriction of(ns-r)plane which is far severe than the one in a generic non-minimal quartic inflationary set up.