Can we learn about New Physics with astronomical and astroparticle data? Since its launch in 2008, the Large Area Telescope, onboard of the Fermi Gamma-ray Space Telescope, has detected the largest amount of gamma rays
in the 20MeV–300 GeV energy range and electrons + positrons in the 7GeV–1TeV range. These impressive statistics allow one to perform a very sensitive indirect experimental search for dark matter. We will present the latest results on these searches and the comparison with LHC searches
