Stochastic fluctuations of bosonic dark matter
  Numerous theories extending beyond the standard model of particle physics
predict the existence of bosons that could constitute the dark matter (DM)
permeating the universe. In the standard halo model (SHM) of galactic dark
matter the velocity distribution of the bosonic DM field defines a
characteristic coherence time $\tau_c$. Until recently, laboratory experiments
searching for bosonic DM fields have been in the regime where the measurement
time $T$ significantly exceeds $\tau_c$, so null results have been interpreted
as constraints on the coupling of bosonic DM to standard model particles with a
bosonic DM field amplitude $\Phi_0$ fixed by the average local DM density.
However, motivated by new theoretical developments, a number of recent searches
probe the regime where $T\ll\tau_c$. Here we show that experiments operating in
this regime do not sample the full distribution of bosonic DM field amplitudes
and therefore it is incorrect to assume a fixed value of $\Phi_0$ when
inferring constraints on the coupling strength of bosonic DM to standard model
particles. 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 (VULF). The constraints inferred from
several previous null experiments searching for ultralight bosonic DM were
overestimated by factors ranging from 3 to 10 depending on experimental
details, model assumptions, and choice of inference framework.
