Are stealth scalar fields stable?

TL;DR

This paper investigates the stability of stealth scalar fields in scalar-tensor gravity, analyzing analytical solutions in different theories and identifying parameter regions of stability and instability.

Contribution

It provides a stability analysis of stealth scalar fields in scalar-tensor theories, including Brans-Dicke gravity, using a covariant and gauge-invariant formalism.

Findings

Certain parameter regions yield stable solutions.

Other regions exhibit instability under tensor perturbations.

Homogeneous perturbations also analyzed for Brans-Dicke solutions.

Abstract

Non-gravitating (stealth) scalar fields associated with Minkowski space in scalar-tensor gravity are examined. Analytical solutions for both non-minimally coupled scalar field theory and for Brans-Dicke gravity are studied and their stability with respect to tensor perturbations is assessed using a covariant and gauge-invariant formalism developed for alternative gravity. For Brans-Dicke solutions, the stability with respect to homogeneous perturbations is also studied. There are regions of parameter space corresponding to stability and other regions corresponding to instability.