Gravitino dark matter and flavor symmetries

In supersymmetric theories without R-parity, the gravitino can play the role of a decaying Dark Matter candidate without the problem of late NLSP decays affecting Big Bang Nucleosynthesis. In this work, we elaborate on recently discussed limits on R- parity violating couplings from decays to antideuterons and discuss the implications for two classes of flavor symmetries: horizontal symmetries, and Minimal Flavor Violation. In most of the parameter space the antideuteron constraints on R-parity violating couplings are stronger than low-energy baryon-number-violating processes. Even in the absence of flavor symmetries, we find strong new limits on couplings involving third-generation fields, and discuss the implications for LHC phenomenology. For TeV scale superpartners, we find that the allowed MFV parameter space is a corner with gravitino masses smaller than O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document}(10) GeV and small tan β.