Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom

TL;DR

This paper reviews methods to identify and analyze the extra degrees of freedom in higher-order gravity theories, which are modifications of Einstein's gravity with additional curvature terms relevant to cosmology and quantum gravity.

Contribution

It provides a comprehensive review of formal and example-based methods for diagnosing and reformulating the extra degrees of freedom in higher-curvature gravity models.

Findings

Comparison of different methods for degree of freedom identification

Discussion of merits and pitfalls of each approach

Clarification of the representation of dynamical variables in modified gravity

Abstract

Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples of such modifications. These theories exhibit, in general, more degrees of freedom than those found in standard General Relativity; counting, identifying, and retrieving the description/representation of such dynamical variables is currently an open problem, and a decidedly nontrivial one. In this work we review, via both formal arguments and custom-made examples, the most relevant methods to unveil the gravitational degrees of freedom of a given model, discussing the merits, subtleties and pitfalls of the various approaches.