Some simple theories of gravity with propagating nonmetricity

TL;DR

This paper explores symmetric Metric-Affine Theories of Gravity, identifying conditions under which these theories predict a healthy massive particle alongside the graviton, focusing on operators up to dimension four.

Contribution

It extends previous work by deriving conditions for propagating nonmetricity in symmetric theories, focusing on a comprehensive class of operators relevant to flat space.

Findings

Conditions for a healthy massive particle with the graviton

Identification of relevant operators up to dimension four

Extension of antisymmetric case results to symmetric theories

Abstract

We investigate symmetric Metric-Affine Theories of Gravity with a Lagrangian containing all operators of dimension up to four that are relevant to free propagation in flat space. Complementing recent work in the antisymmetric case, we derive the conditions for the existence of a single massive particle with good properties, in addition to the graviton.