Abstract

Consistency with quantum gravity can have non-trivial implications at low energies. The Swampland program aims to determine the constraints that any EFT should satisfy to be consistent with a UV quantum gravity completion. In this talk, I will revisit the most important Swampland conjectures that can have implications for Cosmology, especially for inflationary models. In particular, the Swampland Distance Conjecture (SDC) restricts the geodesic distances that scalars can traverse in EFTs as they approach points at infinite distance in moduli space. We propose that, when applied to the subset of light fields in effective theories with scalar potentials, the SDC restricts the amount of non-geodesicity allowed for trajectories along valleys of the potential. This is necessary to ensure consistency of the SDC as a valid swampland criterion at any energy scale across the RG flow, and it constrains the inflationary potentials consistent with quantum gravity. I will then compare these bounds with the asymptotic form of the scalar potential of flux string compactifications. Our results suggest that these compactifications lead to the most generic potentials allowing for maximum non-geodesicity of the potential valleys while respecting the SDC along them. These potentials also preserve an asymptotic version of the de Sitter conjecture, which provides a lower bound on the slope of the potential.