Lovelock gravity is equivalent to Einstein gravity coupled to form fields

TL;DR

Lovelock gravity, a higher-derivative theory, can be reformulated as Einstein gravity coupled with form fields, generalizing the known equivalence of f(R) gravity with scalar fields.

Contribution

The paper demonstrates that all Lovelock theories are equivalent to Einstein gravity coupled with p-form gauge fields, extending previous known cases.

Findings

Lovelock gravity can be recast as Einstein gravity with form fields.

This equivalence applies to all Lovelock theories, not just specific cases.

The linearized equations of Lovelock theories have at most two derivatives.

Abstract

Lovelock gravity is a class of higher-derivative gravitational theories whose linearized equations of motion have no more than two time derivatives. Here, it is shown that any Lovelock theory can be effectively described as Einstein gravity coupled to a p-form gauge field. This extends the known example of an f(R) theory of gravity, which can be described as Einstein gravity coupled to a scalar field.