Ghost instabilities and strong coupling in quadratic non-metricity theories

TL;DR

This paper investigates quadratic non-metricity theories in gravity, revealing ghost instabilities and strong coupling issues in most cases, with specific exceptions like STEGR and certain invariant subclasses, but also showing extended degrees of freedom.

Contribution

It provides a comprehensive analysis of perturbations in quadratic non-metricity theories, identifying stability issues and clarifying the degrees of freedom in various subclasses.

Findings

Most quadratic non-metricity theories exhibit ghost instabilities.

STEGR and transverse-diffeomorphism-invariant gravity are exceptions.

Parity-violating extensions propagate more degrees of freedom than expected.

Abstract

We revisit the framework of Newer General Relativity, defined by all independent quadratic invariants of the non-metricity tensor, including the unique quadratic parity-violating term. We analyze linear perturbations around a flat FLRW background and find that the theory generically exhibits ghost instabilities and/ or propagates more degrees of freedom than in the Minkowski limit, signalling strong coupling. There are two notable exceptions: the Symmetric Teleparallel Equivalent of General Relativity (STEGR) and the transverse-diffeomorphism-invariant gravity subclass, both of which are supplemented by the parity-violating operator. However, since the parity-violating term explicitly breaks (transverse) diffeomorphism invariance, we show, using both the Dirac-Bergmann procedure and the Cartan-Kuranishi algorithm, that the parity-violating extension of STEGR propagates eight degrees of freedom at the fully non-linear level.