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.