Some Recent Results on Ricci-Based Gravity Theories

TL;DR

This paper reviews Ricci-Based Gravity theories, highlighting their relation to general relativity, solution-building methods, junction conditions in $f(R)$ models, and current experimental bounds on these theories.

Contribution

It provides a coherent overview of recent developments in Ricci-Based Gravity theories, emphasizing their correspondence with GR and solution construction techniques.

Findings

Existence of a correspondence between RBGs and GR field equations

Methods to construct new solutions using this correspondence

Summary of experimental and observational bounds on RBG parameters

Abstract

Metric-affine theories in which the gravity Lagrangian is built using (projectively invariant) contractions of the Ricci tensor with itself and with the metric (Ricci-Based Gravity theories, or RBGs for short) are reviewed. The goal is to provide a contextualized and coherent presentation of some recent results. In particular, we focus on the correspondence that exists between the field equations of these theories and those of general relativity, and comment on how this can be used to build new solutions of physical interest. We also discuss the formalism of junction conditions in the $f(R)$ case, and provide a brief summary on current experimental and observational bounds on model parameters.