  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-$\alpha$ 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 $\gamma \lesssim 550$.

Cosmology and Nongalactic Astrophysics