Causality and a-theorem Constraints on Ricci Polynomial and Riemann Cubic Gravities

TL;DR

This paper investigates extended Einstein gravity with Ricci polynomials and Riemann cubic terms, deriving constraints on couplings to ensure ghost freedom, causality, and an $a$-theorem, highlighting that these conditions are met starting at quartic order.

Contribution

It provides the first comprehensive analysis of causality and $a$-theorem constraints on Ricci polynomial and Riemann cubic gravities, identifying the order at which these conditions are simultaneously satisfied.

Findings

Ghost-free and $a$-theorem conditions start at quartic order.

Einstein metrics remain solutions with Ricci polynomial extensions.

Causality constraints are automatically satisfied with Ricci polynomials.

Abstract

In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost free, exhibiting an $a$-theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost free and $a$-theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gravities.