Abstract
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 ${T}_{R}\ensuremath{\lesssim}{10}^{7}\text{ }\text{ }\mathrm{GeV}$. We show that a gravitino with mass $\ensuremath{\sim}1\text{ }\text{ }\mathrm{GeV}$ 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 ${m}_{3/2}<1\text{ }\text{ }\mathrm{GeV}$ gravitinos if the $Q$-balls are formed from a $(B\ensuremath{-}L)=0$ condensate, which produces no net baryon asymmetry. Gravitinos with masses in the range $50\text{ }\text{ }\mathrm{eV}\ensuremath{\lesssim}{m}_{3/2}\ensuremath{\lesssim}100\text{ }\text{ }\mathrm{keV}$ produced in this way can act as warm dark matter and can have observable imprint on the small-scale structure.
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