Non-Trivial Vacua in Higher-Derivative Gravitation

TL;DR

This paper explores the complex vacuum structure of higher-derivative gravity theories, revealing multiple stable vacua including deSitter and anti-deSitter solutions, with detailed analysis of their propagating degrees of freedom.

Contribution

It introduces a method to identify new degrees of freedom in higher-derivative gravity and demonstrates the existence of multiple non-trivial vacua in these theories.

Findings

Higher-derivative theories can have multiple stable vacua.

Vacua include deSitter and anti-deSitter solutions.

Elementary excitations include massless gravitons, massive scalars, and ghost-like spin-two fields.

Abstract

A discussion of an extended class of higher-derivative classical theories of gravity is presented. A procedure is given for exhibiting the new propagating degrees of freedom, at the full non-linear level, by transforming the higher-derivative action to a canonical second-order form. For general fourth-order theories, described by actions which are general functions of the scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown that the higher-derivative theories may have multiple stable vacua. The vacua are shown to be, in general, non-trivial, corresponding to deSitter or anti-deSitter solutions of the original theory. It is also shown that around any vacuum the elementary excitations remain the massless graviton, a massive scalar field and a massive ghost-like spin-two field. The analysis is extended to actions which are arbitrary functions of terms of the form $\nabla^{2k}R$, and it is shown that such theories also have a non-trivial vacuum structure.