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

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 $f(R)=R-\frac{2\Lambda }{1+by(R,\Lambda )}$, 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.

12 pages, 5 figures, 6 tables. Comments welcome. Changes match published version

References in corpus (19)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Conditions for the cosmological viability of f(R) dark energy models
• Are f(R) dark energy models cosmologically viable ?
• f(R) Gravity and Chameleon Theories
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• The Clustering of the SDSS Main Galaxy Sample II: Mock galaxy catalogues and a measurement of the growth of structure from Redshift Space Distortions at $z=0.15$
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• On the evolution of density perturbations in f(R) theories of gravity
• Observational constraints on Galileon cosmology
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Growth rate of cosmological perturbations at z ~ 0.1 from a new observational test
• Cosmic history of viable exponential gravity: Equation of state oscillations and growth index from inflation to dark energy era
• Testing Einstein's gravity and dark energy with growth of matter perturbations: Indications for new Physics?
• The WiggleZ Dark Energy Survey: constraining the evolution of Newton's constant using the growth rate of structure

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• Solar System tests and chameleon effect in f (R) gravity
• Joint Analysis of Constraints on f(R) Parametrization from Recent Cosmological Observations
• Viability of general relativity and modified gravity cosmologies using high-redshift cosmic probes
• Scalar-field potential for viable models in $f(R)$ theory
• Cosmological constraints on viable $f(R)$ models using weak lensing