We consider the cosmological moduli problem in the context of high-scale
supersymmetry breaking suggested by the recent discovery of the standard-model
like Higgs boson. In order to solve the notorious moduli-induced gravitino
problem, we focus on the LARGE volume scenario, in which the modulus decay into
gravitinos can be kinematically forbidden. We then consider the Affleck-Dine
mechanism with or without an enhanced coupling with the inflaton, taking
account of possible Q-ball formation. We show that the baryon asymmetry of the
present Universe can be generated by the Affleck-Dine mechanism in LARGE volume
scenario, solving the moduli and gravitino problems. We also find that the
overall volume modulus decays into a pair of the axionic superpartners, which
contribute to the extra relativistic degrees of freedom.Comment: 46 pages; v2: Comments and references added; v3: dilution factor in
the published version corrected, conclusion unchange