Non-thermal Hot Dark Matter from Inflaton/Moduli Decay: The Momentum
  Distribution and Relaxing the Cosmological Mass Bound
  Decay of the inflaton or moduli which dominated the energy density of the
universe at early times leads to a matter to radiation transition epoch. We
consider non-thermal sterile dark matter particles produced as decay product
during such transitions. The particles have a characteristic energy
distribution - that associated with decays taking place in a matter dominated
universe evolving to radiation domination. We primarily focus on the case when
the particles are hot dark matter, and study their effects on the Cosmic
Microwave Background (CMB) and Large Scale Structure (LSS), explicitly taking
into account their non-thermal momentum distribution. Our results for CMB
angular power and linear matter power spectra reveal interesting features -
such as an order of magnitude higher values of hot dark matter mass in
comparison to the thermal case being consistent with the present data. We
observe that this is related to the fact that $\Delta N_{\rm eff}$ and the hot
DM energy density can be independent of each other unlike the case of thermal
or non-resonantly produced sterile hot DM. We also find features in the CMB at
low $\ell$ angular power potentially related to supersonic transmission of hot
dark matter through the photon-baryon plasma.
