Inflationary Gravitational Wave Spectral Shapes as test for Low-Scale Leptogenesis

TL;DR

This work explores low-scale non-thermal resonant leptogenesis in a global $U(1)_{B-L}$ framework where a heavy majoron $\phi$ decays to RHNs, driving leptogenesis and injecting entropy that damps inflationary PGWs. The authors develop a Boltzmann-equation treatment for the coupled dynamics of $\phi$, RHNs, and radiation, classify three scenarios (instantaneous RHN decay, RHN radiation domination, and RHN matter domination) with analytic and numerical estimates of equilibrium temperatures and dilution factors, and introduce transfer-function formalisms for inflationary GW spectra including a two-step entropy-injection case. They compute the resulting GW signatures, quantify SNR forecasts for a suite of future detectors (LISA, DECIGO/ BBO, ET/CE, μ-ARES, etc.), and map the detectable regions in the RHN mass $M_1$ and washout $K$ parameter space across broad majoron masses and decay temperatures. The results indicate that characteristic knee-like features in the PGW spectrum—two kneelikes in the two-step case—alongside robust SNR signals for plausible $M_1$ and $K$ values, can probe or exclude substantial portions of low-scale leptogenesis scenarios, highlighting strong synergy with laboratory searches for heavy neutral leptons and neutrinoless double-beta decay.

Abstract

We study non-thermal resonant leptogenesis in a general setting where a heavy majoron $φ$ decays to right-handed neutrinos (RHNs) whose further out-of-equilibrium decay generates the required lepton asymmetry. Domination of the energy budget of the Universe by the $φ$ or the RHNs alters the evolution history of the primordial gravitational waves (PGW) of inflationary origin, which re-enter the horizon after inflation, modifying the spectral shape. The decays of $φ$ and RHNs release entropy into the early Universe while nearly degenerate RHNs facilitate low and intermediate-scale leptogenesis. A characteristic damping of the GW spectrum resulting in knee-like features would provide evidence for low-scale non-thermal leptogenesis. We explore the parameter space for the lightest right-handed neutrino mass $M_1\in[10^2,10^{14}]$ GeV and washout parameter $K$ that depends on the light-heavy neutrino Yukawa couplings $λ$, in the weak ($K < 1$) and strong ($K > 1$) washout regimes. The resulting novel features compatible with observed baryon asymmetry are detectable by future experiments like LISA and ET. By estimating signal-to-noise ratio (SNR) for upcoming GW experiments, we investigate the effect of the majoron mass $M_φ$ and reheating temperature $T_φ$, which depends on the $φ-N$ Yukawa couplings $y_N$.

Figures (10)

• Figure 1: Feynmann diagrams of $N\rightarrow lH$ decay process at the (a) tree-level and (b)-(c) 1-loop level. (b) represents the vertex contribution and (c) represents the self-energy contribution.
• Figure 2: Final efficiency factor $\kappa_f$ as a function of washout parameter $K$ in thermal and non-thermal leptogenesis. The solid blue and the dashed red curves represent a thermal and vanishing initial abundance of $N_1$ respectively in thermal leptogenesis. Here we used Eq. \ref{['eq:kappaf_thermal']} and \ref{['eq:zB']} for the blue curve while for the red curve, we use Eq. \ref{['eq:kappaf_weak_vanishing']} for $K\ll1$ and interpolate it to the thermal case in the $K\gg1$ regime. The solid magenta and dashed green lines are solutions to the Bolzmann equations \ref{['eq:boltzrho']} for non-thermal leptogenesis with $M_1=10^5$ GeV, $M_\phi=10^7$ GeV for $T_\phi=10^5$ GeV, and $3\times10^4$ GeV respectively.
• Figure 7: Schematics of key events and temperatures for Case (a), (b) and (c). Inflation ends at reheating temperature $T_{\rm RH}$ after which $\phi$ remains in thermal equilibrium till its freeze out temperature $T_f^\phi$. Then $\phi$ becomes non-relativistic and start the first matter-domination epoch at $T_{\rm dom}\sim1\%M_\phi$. This matter-domination ends when $\phi$ decays at $T_\phi$. For case (a), RHNs also instantaneuously decay at $T_\phi$ and leptogenesis occurs before the BBN temperature $T_{\rm BBN}$. In case (b), RHNs dominate as radiation from $T_\phi$ till their decay at $T_N^{\rm rel}$. In case (c), RHNs dominate as radiation till $T_{\rm NR}$ at which point they become non-relativistic and start the second MD epoch. This epoch ends at RHN decay temperature $T_{N_1}$ when leptogenesis occurs.
• Figure 8: Suppressed gravitational spectra of a benchmark Case (a) scenario when RHNs decay instantaneously or Case (b) where RHNs decay relativistically. Here we have taken $r=0.035$, $T_{\rm RH}=10^{13}$ GeV, $M_1=10^5$ GeV, $K=10^{3}$, and varied $T_\phi$ and $M_\phi$. Value of spectral index is $n_T = 0$ (Left) and $n_T = 0.3$ (Right). The gray line shows the standard GW spectrum without any intermediate matter domination. Black solid and dashed lines correspond to $M_\phi = 10^9$ and $3\times10^9$ GeV respectively. The extreme dampening at frequencies above $\sim100$ Hz is due to inflaton decay.
• Figure 9: Same as Fig. \ref{['fig:nTH_CaseA']} but for a benchmark Case (c), "RHN matter domination" scenario. The Left plot shows the dependence of the spectra on $M_1$ and $K$ while the Right plot shows the dependence on $M_\phi$ and $T_\phi$. In the Left plot, the solid and dashed black lines represent $M_1=10^8$ and $3\times10^8$ GeV respectively. In the Right plot, the solid and dashed black lines represent $M_\phi=10^{12}$ and $2\times10^{12}$ GeV respectively.