Physics Review D 97, 024023 (2018)            arXiv link

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

Yue-Zhou Li¹, Hong Lu^1,*, Jun-Bao Wu^{1, 2}

1. Department of Physics, Tianjin University, Tianjin 300350, China

2. Center for High Energy Physics, Peking University, Beijing 100871, China

* (E-mail: mrhonglu@gmail.com )

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.