Gravitino dark matter from Q-ball decays

Affleck-Dine baryogenesis, accompanied by the formation and subsequent decay of Q-balls, can generate both the baryon asymmetry of the Universe and dark matter in the form of gravitinos. The gravitinos from Q-ball decay dominate over the thermally produced population if the reheat temperature T-R less than or similar to 10(7) GeV. We show that a gravitino with mass similar to 1 GeV is consistent with all observational bounds and can explain the baryon-to-dark-matter ratio in the gauge-mediated models of supersymmetry breaking for a wide range of cosmological and Q-ball parameters. Moreover, decaying Q-balls can be the dominant production mechanism for m(3/2) < 1 GeV gravitinos if the Q-balls are formed from a (B - L) = 0 condensate, which produces no net baryon asymmetry. Gravitinos with masses in the range 50 eV less than or similar to m(3/2) less than or similar to 100 keV produced in this way can act as warm dark matter and can have observable imprint on the small-scale structure.