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This paper summarizes the discussions which took place during the PITT-PACC Workshop entitled “Non-Standard Cosmological Epochs and Expansion Histories,” held in Pittsburgh, Pennsylvania, Sept. 5–7, 2024. Much like the non-standard cosmological epochs that were the subject of these discussions, the format of this workshop was also non-standard. Rather than consisting of a series of talks from participants, with each person presenting their own work, this workshop was instead organized around free-form discussion blocks, with each centered on a different overall theme and guided by a different set of Discussion Leaders. This document is not intended to serve as a comprehensive review of these topics, but rather as an informal record of the discussions that took place during the workshop, in the hope that the content and free-flowing spirit of these discussions may inspire new ideas and research directions. 

Abstract If dark matter resides in a hidden sector minimally coupled to the Standard Model, another particle within the hidden sector might dominate the energy density of the early universe temporarily, causing an early matter-dominated era (EMDE). During an EMDE, matter perturbations grow more rapidly than they would in a period of radiation domination, which leads to the formation of microhalos much earlier than they would form in standard cosmological scenarios. These microhalos boost the dark matter annihilation signal, but this boost is highly sensitive to the small-scale cut-off in the matter power spectrum. If the dark matter is sufficiently cold, this cut-off is set by the relativistic pressure of the particle that dominates the hidden sector. We determine the evolution of dark matter density perturbations in this scenario, obtaining the power spectrum at the end of the EMDE. We analyze the suppression of perturbations due to the relativistic pressure of the dominant hidden sector particle and express the cut-off scale and peak scale for which the matter power spectrum is maximized in terms of the properties of this particle. We also supply transfer functions to relate the matter power spectrum with a small-scale cut-off resulting from the pressure of the dominant hidden sector particle to the matter power spectrum that results from a cold hidden sector. These transfer functions facilitate the quick computation of accurate matter power spectra in EMDE scenarios with initially hot hidden sectors and allow us to identify which models significantly enhance the microhalo abundance. 

Abstract The early universe may have contained internally thermalized dark sectors that were decoupled from the Standard Model. In such scenarios, the relic dark thermal bath, composed of the lightest particle in the dark sector, can give rise to an epoch of early matter domination prior to Big Bang Nucleosynthesis, which has a potentially observable impact on the smallest dark matter structures. This lightest dark particle can easily and generically have number-changing self-interactions that give rise to “cannibal” behavior. We consider cosmologies where an initially sub-dominant cannibal species comes to temporarily drive the expansion of the universe, and we provide a simple map between the particle properties of the cannibal species and the key features of the enhanced dark matter perturbation growth in such cosmologies. We further demonstrate that cannibal self-interactions can determine the small-scale cutoff in the matter power spectrum even when the cannibal self-interactions freeze out prior to cannibal domination.