Is the effect of the Sun's gravitational potential on dark matter
  particles observable?
  We consider the effect of the Sun's gravitational potential on the local
phase space distribution of dark matter particles, focusing on its implication
for the annual modulation signal in direct detection experiments. We perform a
fit to the modulation signal observed in DAMA/LIBRA and show that the allowed
region shrinks if Solar gravitational focusing (GF) is included compared to the
one without GF. Furthermore, we consider a possible signal in a generic future
direct detection experiment, irrespective of the DAMA/LIBRA signal. Even for
scattering cross sections close to the current bound and a large exposure of a
xenon target with 270 ton yr it will be hard to establish the presence of GF
from data. In the region of dark matter masses below 40 GeV an annual
modulation signal can be established for our assumed experimental setup,
however GF is negligible for low masses. In the high mass region, where GF is
more important, the significance of annual modulation itself is very low. We
obtain similar results for lighter targets such as Ge and Ar. We comment also
on inelastic scattering, noting that GF becomes somewhat more important for
exothermic scattering compared to the elastic case.
