Gravitational footprints of massive neutrinos and lepton number breaking
  We investigate the production of primordial Gravitational Waves (GWs) arising
from First Order Phase Transitions (FOPTs) associated to neutrino mass
generation in the context of type-I and inverse seesaw schemes. We examine both
"high-scale" as well as "low-scale" variants, with either explicit or
spontaneously broken lepton number symmetry $U(1)_L$ in the neutrino sector. In
the latter case, a pseudo-Goldstone majoron-like boson may provide a candidate
for cosmological dark matter. We find that schemes with softly-broken $U(1)_L$
and with single Higgs-doublet scalar sector lead to either no FOPTs or too weak
FOPTs, precluding the detectability of GWs in present or near future
measurements. Nevertheless, we found that, in the majoron-like seesaw scheme
with spontaneously broken $U(1)_L$ at finite temperatures, one can have strong
FOPTs and non-trivial primordial GW spectra which can fall well within the
frequency and amplitude sensitivity of upcoming experiments, including LISA,
BBO and u-DECIGO. However, GWs observability clashes with invisible Higgs decay
constraints from the LHC. A simple and consistent fix is to assume the
majoron-like mass to lie above the Higgs-decay kinematical threshold. We also
found that the majoron-like variant of the low-scale seesaw mechanism implies a
different GW spectrum than the one expected in the high-scale seesaw. This
feature will be testable in future experiments. Our analysis shows that GWs can
provide a new and complementary portal to test the neutrino mass generation
mechanism.
