Effective potential of scalar–tensor gravity

Abstract

Abstract Effective potential of a scalar field induced by weak gravity is studied. The set of operators providing the leading contribution and preserving the second order of field equations is found. It is shown that only a mass term and a specific Brans–Dicke-like interaction are relevant within such a setup. An explicit form of the potential is found. The model has room for a natural inflationary scenario similar to the well-known case of the Starobinsky inflation. Possible implications for the standard model are highlighted.