Cosmological Probes of Lepton Parity Freeze-in Dark Matter: $\Delta N_{\mathrm{eff}}$ & 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 $NS\sigma$, 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, $T_{\mathrm{rh}}>m_N$, dominantly through the decay of $N$ ($N\to S\sigma$), and (ii) for $T_{\mathrm{EW}}<T_{\mathrm{rh}}\ll m_N$, via standard model Higgs ($h$) decay ($h\to SS$ 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 $⟨\sigma ⟩=0$. Alternatively, if $\sigma -h$ coupling is small, then $\sigma$ can freeze out with a larger abundance, and hence its decay ($\sigma \to S\nu$) at late epochs can give rise to additional relativistic degrees of freedom ($\Delta N_{\mathrm{eff}}$). Thus, the framework gives a viable DM with mass range varying from MeV to TeV and leaves observable imprints, via gravitational waves and $\Delta N_{\mathrm{eff}}$, which offer complementary probes, potentially detectable in future gravitational wave and CMB experiments.

v2: 16 pages, 13 captioned figures, 1 table, matches published version in NPB

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