  We investigate the modifications in the neutrino flavor oscillations under
the influence of a stochastic gravitational wave background (SGWB), in a
scenario in which General Relativity is modified by an additional Chern-Simons
(CS) term. Assuming that the dark matter halo is in the form of axions, the CS
coupling modifies the pattern of the neutrino flavor oscillations at Earth up
to a total suppression in some frequency range. At the same time, the SGWB in
the halo could stimulate the axion decay into gravitons over a narrow frequency
range, leading to a potentially detectable resonance peak in the enhanced SGWB
strain. A consistent picture would require these features to potentially show
up in neutrino detection from supernovae, gravitational wave detectors, and
experiments aimed at the search for axions in the Milky Way halo.
