$Q$-curvature and gravity

TL;DR

This paper explores a family of higher-curvature gravity theories based on conformal invariants related to the Branson Q-curvature, examining their properties and connections to existing theories in physics.

Contribution

It introduces a new class of conformal invariant gravity theories generalizing the Branson Q-curvature to higher dimensions and analyzes their relation to known higher-curvature models.

Findings

Theories include special conformal invariant cases in even dimensions.

Connections established between these theories and existing higher-curvature models.

Analysis of properties and potential physical implications of these theories.

Abstract

In this paper, we consider a family of $n$-dimensional, higher-curvature theories of gravity whose action is given by a series of dimensionally extended conformal invariants. The latter correspond to higher-order generalizations of the Branson $Q$-curvature, which is an important notion of conformal geometry that has been recently considered in physics in different contexts. The family of theories we study here includes special cases of conformal invariant theories in even dimensions. We study different aspects of these theories and their relation to other higher-curvature theories present in the literature.