Stochastic fluctuations of bosonic dark matter

Numerous theories extending beyond the standard model of particle physics predict the existence of bosons that could constitute dark matter. In the standard halo model of galactic dark matter, the velocity distribution of the bosonic dark matter field defines a characteristic coherence time τ(c). Until recently, laboratory experiments searching for bosonic dark matter fields have been in the regime where the measurement time T significantly exceeds τ(c), so null results have been interpreted by assuming a bosonic field amplitude Φ(0) fixed by the average local dark matter density. Here we show that experiments operating in the T ≪ τ(c) regime do not sample the full distribution of bosonic dark matter field amplitudes and therefore it is incorrect to assume a fixed value of Φ(0) when inferring constraints. Instead, in order to interpret laboratory measurements (even in the event of a discovery), it is necessary to account for the stochastic nature of such a virialized ultralight field. The constraints inferred from several previous null experiments searching for ultralight bosonic dark matter were overestimated by factors ranging from 3 to 10 depending on experimental details, model assumptions, and choice of inference framework.