  We consider the Big Bang Nucleosynthesis (BBN) bounds on light dark matter
whose cross section off nucleons is sufficiently large to enable acceleration
by scattering off of cosmic rays in the local galaxy. Such accelerated DM could
then deposit energy in terrestrial detectors. Since this signal involves DM of
mass ~ keV - 100 MeV and requires large cross sections > 10^-31 cm^2 in a
relativistic kinematic regime, we find that the DM population in this scenario
is generically equilibrated with Standard Model particles in the early
universe. For sufficiently low DM masses < 10 MeV, corresponding to the bulk of
the favored region of many cosmic-ray upscattering studies, this equilibrated
DM population adds an additional component to the relativistic energy density
around T ~ few MeV and thereby spoils the successful predictions of BBN. In the
remaining ~ 10-100 MeV mass range, the large couplings required in this
scenario are either currently excluded or within reach of current or future
accelerator-based searches.
