Gravitational Positivity Bounds on Scalar Potentials

Toshifumi Noumi, Junsei Tokuda

Published 2021-05-04Version 1

We derive constraints on scalar field theories coupled to gravity by using recently developed positivity bounds in the presence of gravity. It is found that a canonically-normalized real scalar cannot have an arbitrarily flat potential unless some new physics enters well below the Planck scale. An upper bound on the scale of new physics is determined by the self-energy corrections to the dispersion relation. Our result provides a swampland condition for scalar potentials.