In seesaw mechanism, if right handed (RH) neutrino masses are generated dynamically by a gauged U(1) symmetry breaking, a stochastic gravitational wave background (SGWB) sourced by a cosmic string network could be a potential probe of leptogenesis. We show that the leptogenesis mechanism that facilitates the dominant production of lepton asymmetry via the quantum effects of right-handed neutrinos in gravitational background, can be probed by GW detectors as well as next-generation neutrinoless double beta decay (0νββ) experiments in a complementary way. We infer that for a successful leptogenesis, an exclusion limit on f − ΩGWh2 plane would correspond to an exclusion on the |mββ| − m1 plane as well. We consider a normal light neutrino mass ordering and discuss how recent NANOGrav pulsar timing data (if interpreted as GW signal) e.g., at 95% CL, would correlate with the potential discovery or null signal in 0νββ decay experiments.

Ultralight primordial black holes (PBHs)(≲109g) completely evaporate via Hawking radiation (HR) and produce all the particles in a given theory regardless of their other interactions. If the right handed (RH) neutrinos are produced from PBH evaporation, successful baryogenesis via leptogenesis predicts mass scale of RH neutrinos as well as black holes. We show that, given the lepton number violation (generation of RH neutrino masses) in the theory is a consequence of a gauged U(1) breaking which is then followed by the formation of PBHs, a network of cosmic strings naturally gives rise to strong stochastic gravitational wave (GW) signal at the sensitivity level of pulsar timing arrays (PTA) and LIGO5. Besides, due to a transient period of black hole domination in the early universe, for which baryon asymmetry is independent of initial PBH density, a break in the GW spectra occurs around MHz frequency. Therefore, to observe the break along with the usual GW signal by the emission of gravitons via HR, GW detectors at higher frequencies are called for. The recent finding by the NANOGrav PTA of a stochastic common spectrum process (interpreted as GWs) across many pulsars is in tension with PBH baryogenesis for large cosmic string loops (α ≃ 0.1).

Within the Type-I seesaw mechanism, quantum effects of the right-handed (RH) neutrinos in the gravitational background lead to an asymmetric propagation of lepton and anti-leptons which induces a Ricci scalar and neutrino Dirac-Yukawa coupling dependent chemical potential and therefore a lepton asymmetry in equilibrium. At high temperature, lepton number violating scattering processes try to maintain a dynamically generated lepton asymmetry in equilibrium. However, when the temperature drops down, the interactions become weaker, and the asymmetry freezes out. The frozen out asymmetry can act as a pre-existing asymmetry prior to the standard Fukugita-Yanagida leptogenesis phase (Ti ∼ Mi, where Mi is the mass of ith RH neutrino). It is then natural to consider the viability of gravitational leptogenesis for a given RH mass spectrum which is not consistent with successful leptogenesis from decays. Primary threat to this gravity-induced lepton asymmetry to be able to successfully reproduce the observed baryon-to-photon ratio is the lepton number violating washout processes at Ti ∼ Mi. In a minimal seesaw set up with two RH neutrinos, these washout processes are strong enough to erase a pre-existing asymmetry of significant magnitude. We show that when effects of flavour on the washout processes are taken into account, the mechanism opens up the possibility of successful leptogenesis (gravitational) for a mass spectrum M2 » 109GeV » M1 with M1 ≳ 6.3 × 106 GeV. We then briefly discuss how, in general, the mechanism leaves its imprints on the low energy CP phases and absolute light neutrino mass scale.

On the frequency-amplitude plane, Gravitational Waves (GWs) from cosmic strings show a flat plateau at higher frequencies due to the string loop dynamics in standard radiation dominated post-inflationary epoch. The spectrum may show an abrupt upward or a downward trend beyond a turning point frequency f*, if the primordial dark age prior to the Big Bang Nucleosynthesis (BBN), exhibits non-standard cosmic histories. We argue that such a spectral break followed by a rising GW amplitude which is a consequence of a post-inflationary equation of state (ω > 1/3) stiffer than the radiation (ω = 1/3), could also be a strong hint of a leptogenesis in the seesaw model of neutrino masses. Dynamical generation of the right handed (RH) neutrino masses by a gauged U(1) symmetry breaking leads to the formation of a network of cosmic strings which emits stochastic GWs. A gravitational interaction of the lepton current by an operator of the form ∂μRjμ — which can be generated in the seesaw model at the two-loop level through RH neutrino mediation, naturally seeks a stiffer equation of state to efficiently produce baryon asymmetry proportional to 1 − 3ω. We discuss how GWs with reasonably strong amplitudes complemented by a neutrino-less double beta decay signal could probe the onset of the most recent radiation domination and lightest RH neutrino mass at the intermediate scales.

A long-lived scalar field (Φ) which couples weakly to the right-handed (RH) neutrinos (NRi), generates small RH neutrino masses (Mi) in Low-Scale-Leptogenesis (LSL) mechanisms, despite having a large vacuum expectation value vΦ. In this case, the correlation shared by the Mis and the duration of the non-standard cosmic history driven by the Φ provides an excellent opportunity to study LSL signatures on primordial gravitational waves (GWs). We find it engaging, specifically for the gravitational waves that originate due to the inflationary blue-tilted tensor power spectrum and propagate through the non-standard cosmic epoch. Depending on Mi, broadly, the scenario has two significant consequences. First, if LSL is at play, GWs with a sizeable blue tilt do not contradict the Big-Bang-Nucleosynthesis (BBN) bound even for the post-inflationary models with very high-scale reheating. Second, it opens up a possibility to probe LSLs via a low-frequency and a complementary high-frequency measurement of GW-spectral shapes which are typically double-peaked. For a case study, we consider the recent results on GWs from the Pulsar-Timing-Arrays (PTAs) as a ‘measurement’ at the low frequencies and forecast the signatures of LSL mechanisms at the higher frequencies.