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

TL;DR

The paper addresses how a minimal extension of the type-I seesaw with a residual lepton parity can yield a viable freeze-in dark matter candidate, connected to resonant leptogenesis and potentially observable signals. It studies two cosmological histories: high reheat temperature $T_{\rm rh}>m_{N_1}$ where DM arises mainly from $N_1\to S\sigma$ decay, and a lower reheat temperature $T_{\rm EW}<T_{\rm rh}\ll m_{N_1}$ where Higgs decays $h\to SS$ produce DM. A key insight is that a large Higgs-portal coupling $\lambda_{h\sigma}$ can trigger a first-order electroweak phase transition, generating stochastic gravitational waves detectable by DECIGO/BBO, while a small $\lambda_{h\sigma}$ allows late $\sigma$ decays to enhance $\Delta N_{ m eff}$, with current and future CMB experiments constraining these scenarios. The framework thus provides a unified link between DM genesis, leptogenesis, gravitational waves, and cosmological radiation content, offering complementary probes for upcoming GW and CMB missions.

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 $σ$ allows for the coupling $N S σ$, 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 $N$ ($N\rightarrow Sσ$), 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 $σ-h$ quartic coupling is large, then it can lead to a strong first-order electroweak phase transition even if $\langleσ\rangle=0$. Alternatively, if $σ-h$ coupling is small, then $σ$ can freeze out with a larger abundance, and hence its decay ($σ\rightarrow Sν$) at late epochs can give rise to additional relativistic degrees of freedom ($Δ{N}_{\rm eff}$). Thus, the framework gives a viable DM with mass range varying from MeV to TeV and leaves observable imprints, via gravitational waves and $Δ{N}_{\rm eff}$, which offer complementary probes, potentially detectable in future gravitational wave and CMB experiments.

Figures (14)

• Figure 1: Parameter space (shown by black dotted points) of first-order EWPT in the plane of $\lambda_{h\sigma}$ vs $m_\sigma$.
• Figure 2: Peak GW amplitude as a function of peak frequency.
• Figure 3: Cosmological evolution of the abundances of $N_1,\sigma$, and $S$. The corresponding equilibrium abundances are shown with the dashed line. The parameters are fixed at {$m_{N_1}=10^{4}$ GeV, $m_\sigma=729.1$ GeV, $\lambda_{h\sigma}=6.63$, $m_S=100$ GeV, $y_{NS}=1.56\times10^{-11}$, $\delta{M}=2.1\times10^{-4}$ GeV,$\gamma=0.15-i0.15$}.
• Figure 4: Correct DM relic contours in the plane of $y_{NS}$ vs $m_S$ for fixed $m_{N_1}=10^{6}$ GeV (black solid) and $m_{N_1}=10^{4}$ GeV (black dashed). The correct lepton asymmetry is generated for $\delta{M}=0.521$ GeV for $m_{N_1}=10^6$ GeV and $\delta{M}=2.1\times10^{-4}$ GeV for $m_{N_1}=10^4$ GeV. The rotation angle is fixed at $\gamma=0.15-i0.15$. The region of thermalization of DM is shown with gray shading for these two masses, respectively. The blue shaded region corresponds to $m_S>m_\sigma$.
• Figure 5: Gravitational wave spectrum from first order electroweak phase transition for BP1, BP2, and BP3 as mentioned in Fig. \ref{['fig:gwamp']}.