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

Abstract

We study the left-right symmetric extension of the Standard Model (LRSM), featuring a TeV-scale right-handed (RH) gauge boson $W_R$ and three RH neutrinos. This setup naturally realises the type-II seesaw mechanism for active neutrino masses. We identify 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 constrain the lightest active neutrino mass to 8.59 x 10^{-10} eV < m_{\nu_1} < 5.06 x 10^{-9} eV$. The resulting frequency-dependent suppression of the stochastic gravitational wave (GW) background is set by the mass and lifetime of the heavier RH neutrinos. Computing the signal-to-noise ratio (SNR) for future detectors, we find 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.