Accidental gauge symmetries of Minkowski spacetime in Teleparallel theories

TL;DR

This paper develops a framework to analyze non-linear teleparallel gravity theories around Minkowski space, revealing that certain gauge symmetries are accidental and that only the massless spin-2 mode propagates at linear order.

Contribution

It introduces a unified Einstein frame for various teleparallel theories and shows how accidental gauge symmetries explain the absence of extra propagating modes around Minkowski.

Findings

All non-linear extensions share the same quadratic action around Minkowski.

Accidental gauge symmetries emerge in the linear theory, explaining the lack of additional modes.

The conformal mode can be absorbed and disappears from the linear spectrum.

Abstract

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein--Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in $f(R)$ theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.