  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. 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-neutrino mass scale. In particular, a two-flavour (three-flavour)
leptogenesis regime is expected to leave distinct imprints in the mHz ($\mu$Hz)
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 index $n_T$.
Interestingly, a three-flavour leptogenesis regime can offer a unique signal
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.
