Aspects of general higher-order gravities

Understand

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.