Aspects of general higher-order gravities

TL;DR

This paper explores higher-order gravity theories based on Riemann tensor contractions, analyzing their linearized equations, constructing quartic curvature models, and examining their gravitational potentials, radiation, and thermodynamics across arbitrary dimensions.

Contribution

It provides a comprehensive classification of Riemann-based higher-order gravities, constructs new quartic models, and extends gravitational analysis to arbitrary dimensions with explicit formulas.

Findings

Classified spectrum of Riemann-based gravity theories.

Constructed quartic extensions of Einsteinian cubic gravity.

Derived generalized Newton potential and gravitational radiation formulas.

Abstract

We study several aspects of higher-order gravities constructed from general contractions of the Riemann tensor and the metric in arbitrary dimensions. First, we use the fast-linearization procedure presented in arXiv:1607.06463 to obtain the equations satisfied by the metric perturbation modes on a maximally symmetric background in the presence of matter and to classify $\mathcal{L}($Riemann$)$ theories according to their spectrum. Then, we linearize all theories up to quartic order in curvature and use this result to construct quartic versions of Einsteinian cubic gravity (ECG). In addition, we show that the most general cubic gravity constructed in a dimension-independent way and which does not propagate the ghost-like spin-2 mode (but can propagate the scalar) is a linear combination of $f($Lovelock$)$ invariants, plus the ECG term, plus a New ghost-free gravity term. Next, we construct the generalized Newton potential and the Post-Newtonian parameter $\gamma$ for general $\mathcal{L}($Riemann$)$ gravities in arbitrary dimensions, unveiling some interesting differences with respect to the four-dimensional case. We also study the emission and propagation of gravitational radiation from sources for these theories in four dimensions, providing a generalized formula for the power emitted. Finally, we review Wald's formalism for general $\mathcal{L}($Riemann$)$ theories and construct new explicit expressions for the relevant quantities involved. Many examples illustrate our calculations.