Can metric-affine gravity be saved?

TL;DR

This paper investigates the conditions under which metric-affine gravity can serve as a consistent quantum theory, emphasizing the importance of symmetry constraints to eliminate unphysical modes and identify viable models.

Contribution

It introduces a symmetry-first approach to determine viable metric-affine gravity models free of ghosts and tachyons, focusing on parity-preserving cases with symmetric distortions.

Findings

Only massless spin-one and spin-three modes are possible besides the graviton.

Gauge symmetries generated by a scalar field do not yield viable models.

Symmetry constraints are crucial for model viability.

Abstract

Like general relativity, metric-affine gravity should be a viable effective quantum theory, otherwise it is a mathematical curiosity without physical application. Assuming a perturbative quantum field theory, the universal, flat limit of metric-affine gravity offers a good foundation for model-building only when symmetry constraints are themselves sufficient to get rid of ghosts and tachyons in the spectrum of propagating particle states, without requiring any further tuning of the couplings. Using this symmetry-first criterion, we find that for parity-preserving models with a totally symmetric distortion, only massless spin-one and spin-three modes are possible besides the graviton. Moreover, no viable models result from gauge symmetries generated by a scalar field.