Generalized ghost-free quadratic curvature gravity

TL;DR

This paper develops a comprehensive framework for covariant quadratic curvature gravity theories, including non-local, ghost-free, asymptotically free models, with detailed equations of motion and validation tests.

Contribution

It introduces a general algorithm for deriving equations of motion in complex quadratic curvature gravity theories, including non-local and infinite derivative models.

Findings

Derived equations of motion for general quadratic curvature actions

Validated equations through Bianchi identities and weak-field tests

Explored a subclass of ghost-free, asymptotically free gravity models

Abstract

In this paper we study the most general covariant action of gravity up to terms that are quadratic in curvature. In particular this includes non-local, infinite derivative theories of gravity which are ghost-free and exhibit asymptotic freedom in the ultraviolet. We provide a detailed algorithm for deriving the equations of motion for such actions containing an arbitrary number of the covariant D'Alembertian operators, and this is our main result. We also perform a number of tests on the field equations we derive, including checking the Bianchi identities and the weak-field limit. Lastly, we consider the special subclass of ghost and asymptotically free theories of gravity by way of an example.