Nonadiabatic cosmological production of ultralight dark matter

Abstract

We study the nonadiabatic cosmological production of ultralight dark matter (ULDM) under a minimal set of assumptions: a free ultralight real scalar as a spectator field in its Bunch-Davies vacuum state during inflation and instantaneous reheating into a radiation dominated era. For ULDM fields minimally coupled to gravity, nonadiabatic particle production yields a distribution function peaked at low comoving momentum ${\mathcal{N}}_{k}\ensuremath{\propto}1/{k}^{3}$. The infrared behavior is a remnant of the infrared enhancement of light minimally coupled fields during inflation. We obtain the full energy momentum tensor, show explicitly its equivalence with the fluid-kinetic one in the adiabatic regime, and extract the abundance, equation of state, and free-streaming length (cutoff in the matter power spectrum). Taking the upper bound on the scale of inflation from Planck, the ULDM saturates the dark matter abundance for $m\ensuremath{\simeq}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{eV}$ with an equation of state parameter $w\ensuremath{\simeq}{10}^{\ensuremath{-}14}$ and a free-streaming length ${\ensuremath{\lambda}}_{\mathrm{fs}}\ensuremath{\simeq}70\text{ }\text{ }\mathrm{pc}$. Thus this cosmologically produced ULDM yields a cold dark matter particle. We argue that the abundance from nonadiabatic production yields a lower bound on generic ULDM and axionlike particles that must be included in any assessment of ULDM as a dark matter candidate.

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