Cosmological constraints and comparison of viable $f(R)$ models

TL;DR

This paper constrains various $f(R)$ gravity models using recent cosmological data, introducing a new class of models that interpolate between the cosmological constant and matter-dominated universe, and finds they are compatible with current observations.

Contribution

It introduces a new class of $f(R)$ models that interpolate between $ ext{Lambda}$CDM and matter domination, and provides constraints using latest cosmological data.

Findings

Hu-Sawicki variants are compatible with data

Models can serve as useful toy models for future surveys

Constraints are consistent with General Relativity deviations being small

Abstract

In this paper we present cosmological constraints on several well-known $f(R)$ models, but also on a new class of models that are variants of the Hu-Sawicki one of the form $f(R)=R-\frac{2\Lambda}{1+b\;y(R,\Lambda)}$, that interpolate between the cosmological constant model and a matter dominated universe for different values of the parameter $b$, which is usually expected to be small for viable models and which in practice measures the deviation from General Relativity. We use the latest growth rate, Cosmic Microwave Background, Baryon Acoustic Oscillations, Supernovae type Ia and Hubble parameter data to place stringent constraints on the models and to compare them to the cosmological constant model but also other viable $f(R)$ models such as the Starobinsky or the degenerate hypergeometric models. We find that these kinds of Hu-Sawicki variant parameterizations are in general compatible with the currently available data and can provide useful toy models to explore the available functional space of $f(R)$ models, something very useful with the current and upcoming surveys that will test deviations from General Relativity.