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We consider the effect of the Sun's gravitational potential on the localphase space distribution of dark matter particles, focusing on its implicationfor the annual modulation signal in direct detection experiments. We perform afit to the modulation signal observed in DAMA/LIBRA and show that the allowedregion shrinks if Solar gravitational focusing (GF) is included compared to theone without GF. Furthermore, we consider a possible signal in a generic futuredirect detection experiment, irrespective of the DAMA/LIBRA signal. Even forscattering cross sections close to the current bound and a large exposure of axenon target with 270 ton yr it will be hard to establish the presence of GFfrom data. In the region of dark matter masses below 40 GeV an annualmodulation signal can be established for our assumed experimental setup,however GF is negligible for low masses. In the high mass region, where GF ismore important, the significance of annual modulation itself is very low. Weobtain similar results for lighter targets such as Ge and Ar. We comment alsoon inelastic scattering, noting that GF becomes somewhat more important forexothermic scattering compared to the elastic case.

Is the effect of the Sun's gravitational potential on dark matter particles observable?