  In this paper we study the interplay between the recently proposed F-theory
GUTs and cosmology. Despite the fact that the parameter range for F-theory GUT
models is very narrow, we find that F-theory GUTs beautifully satisfy most
cosmological constraints without any further restrictions. The viability of the
scenario hinges on the interplay between various components of the axion
supermultiplet, which in F-theory GUTs is also responsible for breaking
supersymmetry. In these models, the gravitino is the LSP and develops a mass by
eating the axino mode. The radial component of the axion supermultiplet known
as the saxion typically begins to oscillate in the early Universe, eventually
coming to dominate the energy density. Its decay reheats the Universe to a
temperature of ~ 1 GeV, igniting BBN and diluting all thermal relics such as
the gravitino by a factor of ~ 10^(-4) - 10^(-5) such that gravitinos
contribute a sizable component of the dark matter. In certain cases,
non-thermally produced relics such as the axion, or gravitinos generated from
the decay of the saxion can also contribute to the abundance of dark matter.
Remarkably enough, this cosmological scenario turns out to be independent of
the initial reheating temperature of the Universe. This is due to the fact that
the initial oscillation temperature of the saxion coincides with the freeze out
temperature for gravitinos in F-theory GUTs. We also find that saxion dilution
is compatible with generating the desired baryon asymmetry from standard
leptogenesis. Finally, the gravitino mass range in F-theory GUTs is 10-100 MeV,
which interestingly coincides with the window of values required for the decay
of the NLSP to solve the problem of Li(7) over-production.
