Superstring-Inspired Particle Cosmology: Inflation, Neutrino Masses,
  Leptogenesis, Dark Matter & the SUSY Scale
  We develop a string-inspired model for particle cosmology, based on a flipped
SU(5)$\times$U(1) gauge group formulated in a no-scale supergravity framework.
The model realizes Starobinsky-like inflation, which we assume to be followed
by strong reheating, with the GUT symmetry being broken subsequently by a light
`flaton' field whose decay generates a second stage of reheating. We discuss
the production of gravitinos and the non-thermal contribution made by their
decays to the density of cold dark matter, which is assumed to be provided by
the lightest neutralino. We also discuss the masses of light and heavy
neutrinos and leptogenesis. As discussed previously [1], a key r\^ole is played
by a superpotential coupling between the inflaton, matter and GUT Higgs fields,
called $\lambda_6$. We scan over possible values of $\lambda_6$, exploring the
correlations between the possible values of observables. We emphasize that the
release of entropy during the GUT transition allows large regions of
supersymmetry-breaking parameter space that would otherwise lead to severe
overdensity of dark matter. Furthermore, we find that the Big Bang
nucleosynthesis lower limit on the reheating temperature of $\sim 1$ MeV
restricts the supersymmetry-breaking scale to a range ${\cal O}(10)$ TeV that
is consistent with the absence of supersymmetric particles at the LHC.
