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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 $ΔN_{\rm eff}$ 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.