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

Lucia A. Popa

TL;DR

The paper investigates gravitational wave signatures from a warm dark matter scenario in a left-right symmetric model with a TeV-scale $W_R$ and three RH neutrinos. It links keV-scale sterile neutrino DM production to an early matter domination epoch driven by heavier RH neutrinos, producing entropy dilution that suppresses the stochastic GW background at horizon-entry scales; a blue-tilted tensor spectrum can compensate this suppression and enhance detectability. The authors derive the DM abundance constraints, RH neutrino decay dynamics, and the resulting GW spectral features, showing that the suppression scales encode the masses and lifetimes of $N_2$ and the reheating temperature $T_{RH}$, while a blue tilt can yield $ ext{SNR} > 10$ for LISA, BBO, and DECIGO. Overall, the work forges a testable connection between beyond-Standard-Model neutrino sectors, early-Universe thermodynamics, and gravitational-wave observations, enabling GW astronomy to probe LRSM parameters and reheating physics via a joint DM-GW signature.

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_{ν_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.

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

TL;DR

The paper investigates gravitational wave signatures from a warm dark matter scenario in a left-right symmetric model with a TeV-scale and three RH neutrinos. It links keV-scale sterile neutrino DM production to an early matter domination epoch driven by heavier RH neutrinos, producing entropy dilution that suppresses the stochastic GW background at horizon-entry scales; a blue-tilted tensor spectrum can compensate this suppression and enhance detectability. The authors derive the DM abundance constraints, RH neutrino decay dynamics, and the resulting GW spectral features, showing that the suppression scales encode the masses and lifetimes of and the reheating temperature , while a blue tilt can yield for LISA, BBO, and DECIGO. Overall, the work forges a testable connection between beyond-Standard-Model neutrino sectors, early-Universe thermodynamics, and gravitational-wave observations, enabling GW astronomy to probe LRSM parameters and reheating physics via a joint DM-GW signature.

Abstract

We study the left-right symmetric extension of the Standard Model (LRSM), featuring a TeV-scale right-handed (RH) gauge boson 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_{ν_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.

Paper Structure

This paper contains 11 sections, 23 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Constraints and requirements for DM sterile neutrino production
  3. DM sterile neutrino abundance
  4. Early matter domination (EMD) onset and the entropy dilution
  5. The spectrum of the gravitational waves
  6. Results
  7. DM signatures in the gravitational waves background
  8. Signal-to-noise ratio for GWs experiments
  9. Conclusions
  10. Acknowledgment
  11. References

Figures (5)

  • Figure 1: Evolution of the temperature in the $M_{N_1} - M_{N_2}$ parameter space across different stages, after imposing the conditions given in Eqs. (\ref{['req_Tf']}), (\ref{['MWR']}) and (\ref{['gamma_N2']}). The $N_1$ keV sterile neutrino energy density $\Omega_s$ is also presented.
  • Figure 2: The conditions for the early matter domination (EMD) from Eqs. (\ref{['req_Hdom']}) and (\ref{['BBN_constrain']}) presented in $M_{N_1} - M_{N_2}$ parameter space. Here $\tau_{N_2}=\Gamma^{-1}_{N_2}$ denotes the lifetime of sterile neutrino $N_2$ while $H^{-1}_{dom}$ and $H^{-1}_{BBN}$ correspond to the lifetimes of the EMD phase and of the Big Bang Nucleosynthesis (BBN), respectively.
  • Figure 3: Gravitational wave (GW) energy density spectrum for $n_T=0$. The left plot corresponds to $T_{RH}=10^{15}$ GeV while the right plot presents the results for $T_{RH}~=~10^9$ GeV. In both plots, the GW spectra obtained within the standard model are shown as black dotted lines. The spectra corresponding to scenarios with an early matter domination (EMD) phase are also presented, for the parameter sets $\{M_{N1}(keV)\,,M_{N_2}(GeV)\,,T_{dec}(GeV)\,,\tau_{N_2}(sec.)\}$: $\{1.6,2.7\,,5.72\times10^{-3}\,,0.224\}$ as green dashed lines, and $\{8\,,80\,,3.1610^{-2}\,, 7.07\times 10^{-3}\}$ as green continuous lines. For comparison, the power-law-integrated sensitivity curves (PLISCs) for the future GW experiments ZendoFresh1 such as SKA, PPTA, LISA, DECIGO, and BBO are also shown.
  • Figure 4: The same as in the Figure \ref{['fig3']} for $n_T=0.5$
  • Figure 5: Left: Tensor tilt ($n_T$) sensitivity curves for the future space-based interferometer experiments LISA, BBO, and DECIGO, derived from the corresponding power-law-integrated sensitivity curves (PLISCs), are shown for $r \le 0.035$ (solid lines) and $r \le 0.001$ (dashed lines). Also shown are the current and projected upper bounds on $n_T$ from CMB and BBN observations, together with the upper limit on $n_T$ derived from the VIRGO and LIGO experiments. Right: The allowed region in $(n_T, T_{RH})$ parameter space that yields the signal-to-noise ratio SNR $\ge 10$, obtained for the LISA, BBO, and DECIGO experiments (see also the text).