Accelerated Cosmological Models in Ricci squared Gravity

TL;DR

This paper explores Ricci squared gravity models within the Palatini formalism, deriving modified Einstein and Friedmann equations that can explain cosmic acceleration without dark energy, supported by a bi-metric geometric interpretation.

Contribution

It introduces Ricci squared Lagrangians in the Palatini formalism and demonstrates their equivalence to Ricci scalar models in explaining cosmic acceleration without exotic matter.

Findings

Modified Friedmann equations support w_{eff}<-1

Ricci squared and Ricci scalar theories share similar mathematical structure

Bi-metric spacetime interpretation enhances physical understanding

Abstract

Alternative gravitational theories described by Lagrangians depending on general functions of the Ricci scalar have been proven to give coherent theoretical models to describe the experimental evidence of the acceleration of universe at present time. In this paper we proceed further in this analysis of cosmological applications of alternative gravitational theories depending on (other) curvature invariants. We introduce Ricci squared Lagrangians in minimal interaction with matter (perfect fluid); we find modified Einstein equations and consequently modified Friedmann equations in the Palatini formalism. It is striking that both Ricci scalar and Ricci squared theories are described in the same mathematical framework and both the generalized Einstein equations and generalized Friedmann equations have the same structure. In the framework of the cosmological principle, without the introduction of exotic forms of dark energy, we thus obtain modified equations providing values of w_{eff}<-1 in accordance with the experimental data. The spacetime bi-metric structure plays a fundamental role in the physical interpretation of results and gives them a clear and very rich geometrical interpretation.