You shall not pass! -- explicit diffeomorphism violation "no-go" constraints and discontinuities

TL;DR

This paper investigates the constraints and discontinuities arising from explicit diffeomorphism and Lorentz symmetry breaking in effective field theories of gravity, revealing potential observational issues due to extra gravitational wave polarizations.

Contribution

It generalizes the minimal EFT framework to include terms that can cancel no-go constraints and analyzes the resulting discontinuities and extra gravitational wave polarizations in linearized gravity.

Findings

Certain terms can cancel no-go constraints in linearized gravity.

Explicit symmetry breaking can lead to additional gravitational wave polarizations.

Extra scalar polarization mode is unsuppressed and potentially observable.

Abstract

This paper collects several results in the study of the explicit symmetry-breaking limit of the effective-field theory (EFT) description of diffeomorphism and local Lorentz-symmetry breaking, where we generalize a subset of the EFT framework (the ``minimal" sector). It is well known that no-go constraints may arise in cases of explicit symmetry-breaking in curved spacetime as a consequence of the Bianchi identities; we show in this work that certain terms in the action can be countenanced and used to cancel would-be no-go constraints, at least in the linearized gravity limit. Nonetheless, we go on to find more potential issues, and we show that one particular explicit breaking subset of the EFT, while evading direct no-go constraints, results in a discontinuity - unsuppressed additional polarizations for gravitational waves. In a general treatment of the explicit breaking EFT, but confined to linearized gravity, we explicitly show the existence of an extra degree of freedom, independent of coordinates. We find extra polarizations of gravitational waves in the solutions, with a scalar mode unsuppressed by any coefficient, which could render these cases ruled out by observations.