Probing Leptogenesis and Pre-BBN Universe with Gravitational Waves Spectral Shapes

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 ($\omega>1/3$) stiffer than the radiation ($\omega=1/3$), 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 $\partial_\mu R j^\mu$--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 $1-3\omega$. 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.