Gravitational wave spectral shapes as a probe of long lived right-handed neutrinos, leptogenesis and dark matter. Global versus local B − L cosmic strings

A bstract The scale of the seesaw mechanism is typically much larger than the electroweak scale. This hierarchy can be naturally explained by U(1) B−L symmetry, which after spontaneous symmetry breaking, simultaneously generates Majorana masses for neutrinos and produces a network of cosmic strings. Such strings generate a gravitational wave (GW) spectrum which is expected to be almost uniform in frequency unless there is a departure from the usual early radiation domination. We explore this possibility in Type I, II and III seesaw frameworks, finding that only for Type-I, long-lived right-handed neutrinos (RHN) may provide a period of early matter domination for parts of the parameter space, even if they are thermally produced. Such a period leaves distinctive imprints in the GW spectrum in the form of characteristic breaks and a knee feature, arising due to the end and start of the periods of RHN domination. These features, if detected, directly determine the right-handed neutrino mass M , and associated left-handed effective neutrino mass $$ \overset{\sim }{m} $$ m ~ of the dominating RHN. We find that GW detectors like LISA and ET could probe RHN masses in the range M ∈ [0.1, 10 9 ] GeV and effective neutrino masses in the $$ \overset{\sim }{m} $$ m ~ ∈ [10 −10 , 10 −8 ] eV range. We investigate the phenomenological implications of long-lived right-handed neutrinos for both local and global U(1) B − L strings, focusing on dark matter production and leptogenesis. We map the viable and detectable parameter space for successful baryogenesis and asymmetric dark matter production from right-handed neutrino decays. We derive analytical and semi-analytical relations correlating the characteristic gravitational-wave frequencies to the neutrino parameters $$ \overset{\sim }{m} $$ m ~ and M , as well as to the relic abundances of dark matter and baryons. We find that the detectable parameter space reaches the boundary of hierarchical leptogenesis and encompasses a substantial portion of the near-resonant regime.