What would it take for dark matter to be literally warm?

Abstract

Warm dark matter (WDM) has served as a valuable benchmark for constraining small-scale structure in the past decades. In this note, I examine what it would take for dark matter to be warm in the literal sense assumed by that benchmark, i.e., a thermal relic that decoupled while relativistic. Satisfying current constraints on the WDM mass, which approach the $\sim$10 keV scale, requires one of three possibilities. One possibility is that there were $\sim 10^4$ relativistic degrees of freedom in the thermal bath at the time of decoupling, which is far beyond what is available in the Standard Model or plausible extensions of it. An alternative is that there was a period of early matter domination whose entropy injection diluted the relic density. However, in this scenario, the perturbations would have evolved through an expansion history that was different from the radiation-dominated one assumed in deriving WDM transfer functions. The third possibility is a dark sector that was never in thermal contact with the Standard Model and was simply born colder via asymmetric reheating. All of these possibilities rely on strong coincidences, where physics that has nothing to do with WDM happens to provide the exact initial conditions assumed in a WDM cosmology. Meanwhile, WDM is often used as a proxy for models with self-consistent thermal histories that generically predict the suppression of structure formation on small scales in a way that is both quantitatively and qualitatively different from WDM. I therefore advocate for a transition to more expressive parameterizations and simulation-based methods in order to extract more useful information from the wealth of upcoming data.