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.