Consistent particle physics in metric-affine gravity from extended projective symmetry

TL;DR

This paper introduces an extended projective symmetry in metric-affine gravity that ensures consistent, pathology-free models with potential applications in cosmology and dark matter, featuring a massless graviton and a scalar field.

Contribution

It identifies a new extended projective symmetry and constructs the most general invariant theory, ensuring consistency and revealing novel physical features.

Findings

The theory is free from ghosts and strong coupling issues.

It predicts a massless graviton and a scalar field suitable for inflation.

Contains effective interactions relevant for fermionic dark matter.

Abstract

It is well-known that the Einstein-Hilbert action exhibits a projective invariance in metric-affine gravity, generated by a single vector (just like diffeomorphisms). However, this symmetry offers no protection against formulating inconsistent models, e.g., with ghost and strong coupling problems. In this letter, we observe that non-minimal kinetic terms of Dirac spinors point to a new extended projective (EP) symmetry generated by a pair of vectors. We prove that the most general EP-invariant theory (at most quadratic in field strengths) is naturally free from all pathologies. Its spectrum only features the massless graviton and a single additional scalar field arising from the square of the Holst curvature. The scalar potential is suitable for inflation and our model moreover contains effective 4-Fermi interactions capable of producing fermionic dark matter. Finally, we point out an alternative double-vector symmetry that similarly leads to a healthy theory with a propagating vector field.