Neutrino Masses, Baryon Asymmetry, Dark Matter and the Moduli Problem :   A Complete Framework
  Recent developments in string theory have led to "realistic" string compactifications which lead to moduli stabilization while generating a hierarchy between the Electroweak and Planck scales at the same time. However, this seems to suggest a rethink of our standard notions of cosmological evolution after the end of inflation and before the beginning of BBN. We argue that within classes of realistic string compactifications, there generically exists a light modulus with a mass comparable to that of the gravitino which generates a large late-time entropy when it decays. Therefore, all known mechanisms of generating the baryon asymmetry of the Universe in the literature have to take this fact into account. In this work, we find that it is still possible to naturally generate the observed baryon asymmetry of the Universe as well as light left-handed neutrino masses from a period of Affleck-Dine(AD) leptogenesis shortly after the end of inflation, in classes of realistic string constructions with a minimal extension of the MSSM below the unification scale (consisting only of right-handed neutrinos) and satisfying certain microscopic criteria described in the text. The consequences are as follows. The lightest left-handed neutrino is required to be virtually massless. The moduli (gravitino) problem can be naturally solved in this framework both within gravity and gauge mediation. The observed upper bound on the relic abundance constrains the moduli-matter and moduli-gravitino couplings since the DM is produced non-thermally within this framework. Finally, although not a definite prediction, the framework naturally allows a light right-handed neutrino and sneutrinos around the electroweak scale which could have important implications for DM as well as the LHC. 
Piyush Kumar