Constraining Nonthermal Dark Matter's Impact on the Matter Power Spectrum
The inclusion of a period of (effective) matter domination following inflation and prior to the onset of radiation domination has interesting and observable consequences for structure growth. During this early matter-dominated era (EMDE), the Universe was dominated by massive particles, or an oscillating scalar field, that decayed into Standard Model particles, thus reheating the Universe. This decay process could also be the primary source of dark matter. In the absence of fine-tuning between the masses of the parent and daughter particles, both dark matter particles and Standard Model particles would be produced with relativistic velocities. We investigate the effects of the nonthermal production of dark matter particles with relativistic velocities on the matter power spectrum by determining the resulting velocity distribution function for the dark matter. We find that the vast majority of dark matter particles produced during the EMDE are still relativistic at reheating, so their free streaming erases the perturbations that grow during the EMDE. The free streaming of the dark matter particles can also prevent the formation of satellite galaxies around the Milky Way and the structures observed in the Lyman-$α$ forest. For a given reheat temperature, these observations put an upper limit on the velocity of the dark matter particles at their creation. For example, for a reheat temperature of 10 MeV, dark matter must be produced with a Lorentz factor $γ\lesssim 550$.