  The interaction of neutrinos with ultralight scalar and vector dark matter
backgrounds induce a modification of the neutrino dispersion relation. The
effects of this modification are reviewed in the framework of asymmetric
emission of neutrinos from the supernova core, and, in turn, of pulsar kicks.
We consider the neutrino oscillations, focusing in particular to active-sterile
conversion. The ultralight dark matter induced neutrino dispersion relation
contains a term of the form $\delta {\bf \Omega}\cdot \hat{{\bf{p}}}$, where
$\delta {\bf \Omega}$ is related to the ultralight dark matter field and
$\hat{{\bf p}}$ is the unit vector along the direction of neutrino momentum.
The relative orientation of ${\bf p}$ with respect to $\delta {\bf \Omega}$
affects the mechanism for the generation of the observed pulsar velocities. We
obtain the resonance condition for the active-sterile neutrino oscillation in
ultralight dark matter background and calculate the star parameters in the
resonance surface so that both ultralight scalar and vector dark matter
backgrounds can explain the observed pulsar kicks. The asymmetric emission of
neutrinos in presence of ultralight dark matter background results
gravitational memory signal which can be probed from the future gravitational
wave detectors such as adLIGO (advanced LIGO), adVIRGO (advanced VIRGO), DECIGO
(DECi-hertz Interferometer Gravitational wave Observatory), BBO (Big Bang
Observer), and ET (Einstein Telescope). We also establish a relation between
the ultralight dark matter parameters and the Lorentz and CPT invariance
violation parameters.
