Effective Potential of Scalar-Tensor Gravity

TL;DR

This paper investigates the effective potential of scalar fields in scalar-tensor gravity, identifying key operators and potential forms, with implications for inflation and the Standard Model.

Contribution

It derives the explicit form of the effective potential and highlights the relevance of specific operators, including a Brans-Dicke-like interaction, in scalar-tensor gravity.

Findings

Only the mass term and a specific Brans-Dicke-like interaction are relevant.

The explicit potential form supports natural inflation scenarios.

Implications for Standard Model physics are discussed.

Abstract

Effective potential of a scalar field induced by weak gravity is studied. The set of operators relevant for leading effects and preserving the second order of field equations is found. It is shown that only the mass term and a specific Brans-Dicke-like interaction are relevant within such a setup. The 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.