Inflation from the internal volume in type IIB/F-theory compactification

Abstract

We study the cosmological inflation within a recently proposed framework of perturbative moduli stabilization in type IIB/F-theory compactifications on Calabi–Yau threefolds. The stabilization mechanism utilizes three stacks of magnetized 7-branes and relies on perturbative corrections to the Kähler 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 Kähler 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 stabilization 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. We discuss a class of uplifting potentials arising from strongly coupled matter fields. In a particular case, they reproduce the effect of the new Fayet–Iliopoulos term recently discussed in a supergravity context, that can be written for a non-R-symmetry U(1) and is gauge invariant at the Lagrangian level.