Gravitational Positivity Bounds on Scalar Potentials

Understand

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.