Gravitational Wave Signatures of Warm Dark Matter in the Gauge Extensions of the Standard Model

We studied the left-right symmetric extension of the standard model (LRSM), featuring a TeV-scale, right-handed (RH) gauge boson WR and three RH neutrinos. This setup naturally realizes the type-II seesaw mechanism for active neutrino masses. We identified the conditions that yield sufficient entropy dilution to reconcile the keV sterile neutrino dark matter energy density with observations while inducing an early matter domination (EMD) phase. These constrained the lightest active neutrino mass to 8.59×10−10eV<mν1<5.06×10−9eV. The resulting frequency-dependent suppression of the stochastic gravitational wave (GW) background was set by the mass and lifetime of the heavier RH neutrinos. Computing the signal-to-noise ratio (SNR) for future detectors, we found that a blue-tilted primordial tensor spectrum can boost the GW signal to detectable levels (SNR > 10) in experiments such as LISA, BBO, and DECIGO.