Non-thermal Histories and Implications for Structure Formation
  We examine the evolution of cosmological perturbations in a non-thermal
post-inflationary history with a late-time matter domination period prior to
BBN. Such a cosmology could arise naturally in the well-motivated moduli
scenario in the context of supersymmetry (SUSY) -- in particular in models of
Split-SUSY. Sub-horizon dark matter perturbations grow linearly during the
matter dominated phase before reheating and can lead to an enhancement in the
growth of substructure on small scales, even in the presence of dark matter
annihilations. This suggests that a new scale (the horizon size at reheating)
could be important for determining the primordial matter power spectrum.
However, we find that in many non-thermal models free-streaming effects or
kinetic decoupling after reheating can completely erase the enhancement leading
to small-scale structures. In particular, in the moduli scenario with wino or
higgsino dark matter we find that the dark matter particles produced from
moduli decays would thermalize with radiation and kinetically decouple below
the reheating temperature. Thus, the growth of dark matter perturbations is not
sustained, and the predictions for the matter power spectrum are similar to a
standard thermal history. We comment on possible exceptions, but these appear
difficult to realize within standard moduli scenarios. We conclude that
although enhanced structure does not provide a new probe for investigating the
cosmic dark ages within these models, it does suggest that non-thermal
histories offer a robust alternative to a strictly thermal post-inflationary
history.
