Inflation from the internal volume in type IIB/F-theory compactification
  We study cosmological inflation within a recently proposed framework of
perturbative moduli stabilisation in type IIB/F theory compactifications on
Calabi-Yau threefolds. The stabilisation mechanism utilises three stacks of
magnetised 7-branes and relies on perturbative corrections to the K\"ahler
potential that grow logarithmically in the transverse sizes of co-dimension two
due to local tadpoles of closed string states in the bulk. The inflaton is the
K\"ahler modulus associated with the internal compactification volume that
starts rolling down the scalar potential from an initial condition around its
maximum. Although the parameter space allows moduli stabilisation in de Sitter
space, the resulting number of e-foldings is too low. An extra uplifting source
of the vacuum energy is then required to achieve phenomenologically viable
inflation and a positive (although tiny) vacuum energy at the minimum. Here we
use, as an example, a new Fayet-Iliopoulos term proposed recently in
supergravity that can be written for a non R-symmetry U(1) and is gauge
invariant at the Lagrangian level; its possible origin though in string theory
remains an open interesting problem.
