Aspects of Quadratic Gravity

TL;DR

This paper explores quadratic gravity theories, analyzing their propagating modes, infrared modifications, and connections to fundamental theories like string theory, revealing a complex interplay between UV and IR properties.

Contribution

It provides a detailed analysis of the physical modes in quadratic gravity, clarifies conditions for ghost freedom, and discusses how such theories can emerge from string theory.

Findings

Pure R^2 theory is ghost free.

Flat backgrounds propagate only a scalar mode.

Curved backgrounds recover the graviton mode.

Abstract

We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-theory. We demonstrate that string theory on non-compact $CY_3$ manifolds, like a line bundle over $\mathbb{CP}^2$, may indeed lead to gravity dynamics determined by a higher curvature action.