Gravitational Positivity Bounds on Scalar Potentials

TL;DR

This paper derives bounds on scalar potentials coupled to gravity, showing that extremely flat potentials require new physics below the Planck scale, thus providing a swampland criterion for such theories.

Contribution

It introduces positivity bounds in gravitational scalar theories, establishing limits on potential flatness and linking them to the scale of new physics.

Findings

Flat scalar potentials are constrained by positivity bounds.

New physics must appear below the Planck scale for certain scalar potentials.

Provides a swampland condition for scalar field theories with gravity.

Abstract

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 loop corrections to the self-energy. Our result provides a swampland condition for scalar potentials.