Effective interactions in Ricci-Based Gravity models below the non-metricity scale

Abstract

We show how minimally-coupled matter fields of arbitrary spin, when coupled to Ricci-Based Gravity theories, develop non-trivial effective interactions that can be treated perturbatively only below a characteristic high-energy scale ${\Lambda }_Q$. Our results generalize to arbitrary matter fields those recently obtained for spin 1/2 fields in \cite{Latorre:2017uve}. We then use this interactions to set bounds on the high-energy scale ${\Lambda }_Q$ that controls departures of Ricci-Based Gravity theories from General Relativity. Particularly, for Eddington-inspired Born-Infeld gravity we obtain the strong bound $|\kappa |<3.5\times 10^{-14}{\text{ m}}^5{\text{kg}}^{-1}{\text{s}}^{-2}$.

Comments: 14 pages, 2 figures. We have corrected an error in the translation of the bound from $\Lambda$ to $\kappa$. Some references have been updated as well