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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.