Impact of Warm Dark Matter on the Cosmic Neutrino Background
  Anisotropies
  The Cosmic Neutrino Background (C$\nu$B) anisotropies for massive neutrinos
are a unique probe of large-scale structure formation. The redshift-distance
measure is completely different for massive neutrinos as compared to
electromagnetic radiation. The C$\nu$B anisotropies in massive neutrinos grow
in response to non-relativistic motion in gravitational potentials seeded by
relatively high $k$-modes. Differences in the early phases of large-scale
structure formation in Warm Dark Matter (WDM) versus Cold Dark Matter (CDM)
cosmologies have an impact on the magnitude of the C$\nu$B anisotropies for
contributions to the angular power spectrum that peak at high $k$-modes. We
take the examples of WDM consisting of 2, 3 or 7 keV sterile neutrinos and show
that the C$\nu$B anisotropies for 0.05 eV neutrinos drop off at high-$l$
multipole moment in the angular power spectrum relative to CDM. At the same
angular scales that one can observe baryonic acoustical oscillations in the
CMB, the C$\nu$B anisotropies begin to become sensitive to differences in WDM
and CDM cosmologies. The precision measurement of high-$l$ multipoles in the
C$\nu$B neutrino sky map is a potential possibility for the PTOLEMY experiment
with thin film targets of spin-polarized atomic tritium superfluid that exhibit
significant quantum liquid amplification for non-relativistic relic neutrino
capture.
