Revisiting Stability in New General Relativity

TL;DR

This paper analyzes the stability of New General Relativity theories around Minkowski space, identifying conditions for stable, healthy models that propagate tensor and scalar modes, challenging previous claims of a single viable theory.

Contribution

It reveals three instability-free branches of New General Relativity, including two new stable models with tensor and scalar modes, contradicting prior literature.

Findings

Decoupling case reduces to linearized gravity plus a massless KR field

Vector modes are generally unstable unless they vanish

Identifies three stable branches, including two new models with tensor and scalar modes

Abstract

We study the degrees of freedom in New General Relativity -- flat and metric compatible family of theories -- around the Minkowski background in a gauge invariant manner. First, we confirm the decoupling case, in which the theory reduces to linearized gravity plus a massless KR field. We then show that, unless they vanish, the vector modes of this theory will be unstable. In addition, we find two new branches of the theories, which are instability-free and propagate linearly two tensor modes and in one of the cases also a massless scalar field. This shows that while the generic theory is ill-behaved, there are three possible realizations of instability-free cases, in contradiction to the previous literature, which states that there is only one healthy theory in addition to general relativity.