Probing thermal leptogenesis and dark matter through primordial gravitational waves from a supercooled universe

TL;DR

This work investigates a scale-invariant U(1)_{B-L} extension of the Standard Model in which a supercooled, radiatively induced first-order phase transition generates RHN masses and a strong stochastic gravitational-wave background. Post-transition scalar decays can drive an early matter-dominated epoch, with its duration controlled by the RHN mass M_N and gauge coupling g', thereby reshaping the GW spectrum via entropy production that also imprints an M_N-dependent distortion linked to the leptogenesis flavour regime. The framework accommodates non-thermal RHN dark matter from scalar decay and thermal leptogenesis for the remaining RHNs, and a singlet extension expands the viable parameter space to include the three-flavour regime. The resulting high-frequency GW signals, amplified by supercooling and modified by the MD era, offer a unique observational window into the scale and flavour structure of leptogenesis in future gravitational-wave experiments.

Abstract

We explore the cosmological dynamics of a supercooled first-order phase transition in the classically conformal $U(1)_{B-L}$ extension of the Standard Model, where radiative symmetry breaking simultaneously generates the right-handed neutrino (RHN) masses, and a strong stochastic gravitational-wave (GW) background. The slow decay of the scalar field into RHNs can induce an early matter-dominated (EMD) era whose duration is sensitive to the RHN mass and gauge coupling $g^\prime$. This non-standard cosmological phase reshapes the GW spectrum and leaves a distinctive RHN-mass-dependent spectral distortion that correlates with the flavour regime of thermal leptogenesis. Within this framework, one RHN can serve as a dark matter candidate produced nonthermally from scalar decays, while the remaining states generate the baryon asymmetry via thermal leptogenesis. For $g^\prime=0.5$, we identify such a parameter region, and show that with singlet extensions, even with a smaller gauge coupling, one can realise this mechanism for the three-flavour regime. The resulting GW signals, amplified by supercooling and modified by EMD, provide a unique window to probe the scale and flavour structure of leptogenesis in future high-frequency GW observations.

Figures (4)

• Figure 1: Top-left: The allowed parameter space for RHN-mass controlled matter domination, assuming $P_{\rm NLO}^{(1)}$ friction with $g^\prime=0.5$, is indicated where the green shaded region represents the amount of entropy production after the end of early matter domination. Top-right: The same parameter space as left, but for $P_{\rm NLO}^{(2)}$ friction. Bottom-left: The allowed parameter space for RHN-mass controlled matter domination, assuming $P_{\rm NLO}^{(1)}$ friction with $g^\prime=0.5$, is indicated where the green shaded region represents the RHN dark matter mass required to achieve the correct relic density, $\Omega_{\rm DM}h^2 \simeq 0.12$. Bottom-right: The same parameter space as left, but for $P_{\rm NLO}^{(2)}$ friction.
• Figure 2: Top-left: The allowed parameter space for RHN-mass controlled matter domination with the singlet extension, assuming $P_{\rm NLO}^{(1)}$ friction with $g^\prime=0.1$ and $\lambda_{\Phi S}\in [1.85,2.51]$, is indicated where the green shaded region represents the amount of entropy production after the end of early matter domination. Top-right: The same parameter space as left, but for $P_{\rm NLO}^{(2)}$ friction. Bottom-left:The allowed parameter space for RHN-mass controlled matter domination with the singlet extension, assuming $P_{\rm NLO}^{(1)}$ friction with $g^\prime=0.1$ and $\lambda_{\Phi S}\in [1.85,2.51]$, is indicated where the green shaded region represents the RHN dark matter mass required to achieve the correct relic density, $\Omega_{\rm DM}h^2 \simeq 0.12$. Bottom-right: The same parameter space as left, but for $P_{\rm NLO}^{(2)}$ friction.
• Figure 3: Left: The benchmarks BP1 ($\clubsuit$), BP2 ($\spadesuit$), BP3($\bigstar$) correspond to different flavour regimes of leptogenesis, assuming $P_{\rm NLO}^{(1)}$ friction with $g^\prime=0.1$ and $\lambda_{\Phi S}\in [1.85,2.51]$, where the green shaded region represents the amount of entropy production after the end of early matter domination. Right: The GW spectrum corresponding to the benchmarks on the left is shown as solid lines (with modified reheating) and dashed lines (without modified reheating).
• Figure 4: Left: The variation of $f_{\rm peak}$ with $M_N$ is indicated by the solid(dashed) line for modified(standard) reheating. Right: The effect of varying $M_N$, similar to the left, but projected onto the $f_{\rm peak}$ vs $\Omega_{\rm GW}^{\rm peak}h^2$ plane.