Nonadiabatic cosmological production of ultralight dark matter

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 Nk∝1/k3. 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≃1.5×10−5 eV with an equation of state parameter w≃10−14 and a free-streaming length λfs≃70 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.