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Abstract Cosmology and astrophysics provide various ways to study the properties of dark matter even if they have negligible non-gravitational interactions with the Standard Model particles and remain hidden. We study a type of hidden dark matter model in which the dark matter is completely decoupled from the Standard Model sector except gravitationally, and consists of a single species with conserved comoving particle number and conserved comoving entropy. This category of hidden dark matter includes models that act as warm dark matter but is more general. In particular, in addition to having an independent temperature from the Standard Model sector, it includes cases in which dark matter is in its own kinetic equilibrium or is free-streaming, obeys fermionic or bosonic statistics, and processes a chemical potential that controls the particle occupation number. While the usual parameterization using the free-streaming scale or the particle mass no longer applies, we show that all cases can be well approximated by a set of functions parameterized by only one parameter as long as the chemical potential is nonpositive: the characteristic scale factor at the time of the relativistic-to-nonrelativistic transition. We study the constraints from Big Bang Nucleosynthesis, the cosmic microwave background, the Lyman-α forest, and the smallest halo mass. We show that the most significant phenomenological impact is the suppression of the small-scale matter power spectrum — a typical feature when the dark matter has a velocity dispersion or pressure at early times. So far, the Lyman-α forest and the small dark matter halo population provide the strongest constraints, limiting the transition redshift to be larger than ∼6.2×10⁷. 

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.