  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.
