Recent BABAR results on dark matter and light Higgs searches and on CP and T violation

Recent BABAR results on several topics are presented. We report the observation of T-violation as well as recent results on CP-violation in B decays in a dataset collected at the Y(4S) resonance. We also present searches for low mass CP-odd Higgs bosons, predicted in non-minimal SUSY models, as well as searches for dark-sector gauge bosons motivated by astrophysical observations, using radiative decays of the Y(1S,2S,3S) resonances and other e+e− processes. These searches enable stringent limits to be set on the parameters of such particles