Mirage in the Sky: Non-thermal Dark Matter, Gravitino Problem, and
  Cosmic Ray Anomalies
  Recent anomalies in cosmic rays could be due to dark matter annihilation in
our galaxy. In order to get the required large cross-section to explain the
data while still obtaining the right relic density, we rely on a non standard
thermal history between dark matter freeze-out and Big-Bang Nucleosynthesis
(BBN). We show that through a reheating phase from the decay of a heavy moduli
or even the gravitino, we can produce the right relic density of dark matter if
its self-annihilation cross-section is large enough. In addition to fitting the
recent data, this scenario solves the cosmological moduli and gravitino
problems. We illustrate this mechanism with a specific example in the context
of U(1)_{B-L} extended MSSM where supersymmetry is broken via mirage mediation.
These string motivated models naturally contain heavy moduli decaying to the
gravitino, whose subsequent decay to the LSP can reheat the universe at a low
temperature. The right-handed sneutrino and the B-L gaugino can both be viable
dark matter candidates with large cross-section. They are leptophilic because
of B-L charges. We also show that it is possible to distinguish the non-thermal
from the thermal scenario (using Sommerfeld enhancement) in direct detection
experiments for certain regions of parameter space.
