Critical Points of D-Dimensional Extended Gravities

TL;DR

This paper investigates the parameter space of higher-dimensional Einstein gravity with quadratic curvature terms, identifying critical points where only massless gravitons exist and exploring models with unique vacua and vanishing energy excitations.

Contribution

It introduces the concept of critical points in D-dimensional extended gravities, revealing conditions for unique vacua and massless graviton spectra in these theories.

Findings

Existence of two distinct (A)dS vacua in D>4 dimensions.

Identification of critical points with only massless tensor gravitons.

Construction of a model with a unique vacuum and determined cosmological constant.

Abstract

We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D>4 there are in general two distinct (anti)-de Sitter vacua. We show that for appropriate choice of the parameters there exists a critical point for one of the vacua, for which there are only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl^2 model with a unique vacuum, whose \Lambda is determined.