Tomography of flavoured leptogenesis with primordial blue gravitational waves

We explore a scenario where an early epoch of matter domination is driven by the mass scale $M_N$ of the right-handed neutrinos, which also characterizes the different flavour regimes of leptogenesis. Such a matter-domination epoch gives rise to peculiar spectral imprints on primordial Gravitational Waves (GWs) produced during inflation. We point out that the characteristic spectral features are detectable in multiple frequency bands with current and future GW experiments in case of Blue GWs (BGWs) described by a power-law with a positive spectral index $(n_T >0)$ and an amplitude compatible with Cosmic Microwave Background (CMB) measurements at the CMB scale. We find that the three-flavour leptogenesis regime with $M_N \lesssim 10^9~{\rm GeV}$ imprints BGWs more prominently than the two-flavour and one-flavour regimes characterized by a higher right-handed neutrino mass scale. In particular, a two-flavour (three-flavour) leptogenesis regime is expected to leave distinct imprints in the mHz-Hz ($\mu$Hz-mHz) band. Moreover, we translate the current Big Bang Nucleosynthesis (BBN) and LIGO limits on the GW energy density into constraints on the flavour leptogenesis parameter space for different GW spectral indices $n_T$. We provide a rigorous statistical analysis of how the future GW detectors would be conjointly able to distinguish the flavour regimes. Interestingly, the scenario also offers unique GW signals testable in the next LIGO run with a correlated signature in the PTA frequency band with an amplitude comparable to the one expected from supermassive black holes.