Constraining f(R) gravity in the Palatini formalism

TL;DR

This paper explores $f(R)$ gravity models in the Palatini formalism, considering both positive and negative powers of curvature, to understand their impact on the universe's evolution across all cosmological eras and establish observational constraints.

Contribution

It introduces and analyzes $f(R)$ models with combined positive and negative curvature powers in the Palatini approach, extending previous studies focused mainly on late-time effects.

Findings

Constraints on extra curvature terms derived from cosmological data

Positive powers influence early universe phenomena like inflation

Negative powers affect late-time cosmic acceleration

Abstract

Although several models of $f(R)$ theories of gravity within the Palatini approach have been studied already, the interest was concentrated on those that have an effect on the late-time evolution of the universe, by the inclusion for example of terms inversely proportional to the scalar curvature in the gravitational action. However, additional positive powers of the curvature also provide interesting early-time phenomenology, like inflation, and the presence of such terms in the action is equally, if not more, probable. In the present paper models with both additional positive and negative powers of the scalar curvature are studied. Their effect on the evolution of the universe is investigated for all cosmological eras, and various constraints are put on the extra terms in the actions. Additionally, we examine the extent to which the new terms in positive powers affect the late-time evolution of the universe and the related observables, which also determines our ability to probe their presence in the gravitational action.