Enriched Phenomenology in Extended Palatini Theories

TL;DR

This paper explores extended Palatini gravity theories with Lagrangians involving both R and R_{}R^{}, revealing richer phenomenology and modified dynamics even for traceless sources, unlike simpler models.

Contribution

It demonstrates that f(R,R_{}R^{}) theories have algebraic relations for R and Q depending on energy density and pressure, unlike simpler models.

Findings

R and Q are algebraic functions of energy density and pressure.

Modified dynamics occur even for traceless sources.

f(R,R_{}R^{}) theories differ from f(R) models in phenomenology.

Abstract

We show that extended theories of gravity with Lagrangian f(R,R_{\mu\nu}R^{\mu\nu}) in the Palatini formulation possess a phenomenology much richer than the simpler f(R) or f(R_{\mu\nu}R^{\mu\nu}) theories. In fact, we find that the scalars R and Q=R_{\mu\nu}R^{\mu\nu} can be written as algebraic functions of the energy density and pressure of the energy momentum tensor. In the simpler cases of f(R) or f(R_{\mu\nu}R^{\mu\nu}) theories, R and Q are just functions of the trace T of the energy-momentum tensor. As a result, in radiation dominated universes f(R) and f(R_{\mu\nu}R^{\mu\nu}) theories exhibit the same dynamics as general relativity with an effective cosmological constant. This is not the case of f(R,R_{\mu\nu}R^{\mu\nu}) models, in which R=R(\rho,P) and Q=Q(\rho,P) and, therefore, modified dynamics exists even for traceless sources.