  In neutrinophilic two-Higgs-doublet models, neutrinos acquire mass due to a
Higgs field with vacuum expectation value of the order of 10^{-2} eV,
corresponding to a Compton wavelength in the 10 micrometer range. This creates
a situation in which nonminimal couplings between Higgs fields and spacetime
curvature may lead to novel observable effects. Among these, we discuss the
possibility of variable neutrino masses, with implications for the dependence
of the neutrino oscillation frequency on the spacetime curvature, a further
source of dispersion of the neutrino arrival times from supernovae events, and
possibly also a mechanism leading to gravitationally-induced neutrino
superluminality. Finally, we propose laboratory-scale experiments in which
properly designed electroweak cavities may be used to change neutrino masses,
which should be observable through time of flight experiments.
