Cosmological Probes of Lepton Parity Freeze-in Dark Matter: $\Delta N_{\rm eff}$ & Gravitational Waves

Abstract

In the canonical type-I seesaw mechanism for neutrino masses, a residual symmetry known as lepton parity: $(-1)^L$, remains preserved. Introducing a Majorana fermion $S$ with even lepton parity renders it naturally stable, making it a viable dark matter (DM) candidate. The addition of a lepton parity odd singlet scalar $\sigma$ allows for the coupling $N S \sigma$, where $N$ is the right-handed neutrino. If $S$ is not thermalized, then DM relic can be produced in two distinct ways: (i) for reheating temperature, $T_{\rm rh}>m_{N}$, dominantly through the decay of $N$ ($N\rightarrow S\sigma$), and (ii) for $T_{\rm EW}<T_{\rm rh}\ll m_{N}$, via standard model Higgs ($h$) decay ($h\rightarrow SS$ at one loop). If the $\sigma-h$ quartic coupling is large, then it can lead to a strong first-order electroweak phase transition even if $\langle\sigma\rangle=0$. Alternatively, if $\sigma-h$ coupling is small, then $\sigma$ can freeze out with a larger abundance, and hence its decay ($\sigma\rightarrow S\nu$) at late epochs can give rise to additional relativistic degrees of freedom ($\Delta{N}_{\rm eff}$). Thus, the framework gives a viable DM with mass range varying from MeV to TeV and leaves observable imprints, via gravitational waves and $\Delta{N}_{\rm eff}$, which offer complementary probes, potentially detectable in future gravitational wave and CMB experiments.