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.

arXiv comment12 pages, 5 figures, 6 tables. Comments welcome. Changes match published version

References in corpus (51)

• Planck 2015 results. XIII. Cosmological parameters
• Dynamics of dark energy
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• f(R) theories
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Information criteria for astrophysical model selection
• The WiggleZ Dark Energy Survey: Joint measurements of the expansion and growth history at z < 1
• 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 ?
• The Physics of Cosmic Acceleration
• How many cosmological parameters?
• Reconstructing the history of structure formation using redshift distortions
• Interpreting large-scale redshift-space distortion measurements
• Crossing the Phantom Divide: Theoretical Implications and Observational Status
• 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 $z=0.15$
• Cosmic flows in the nearby universe from Type Ia Supernovae
• The Subaru FMOS galaxy redshift survey (FastSound). IV. New constraint on gravity theory from redshift space distortions at $z\sim 1.4$
• Galaxy And Mass Assembly (GAMA): improved cosmic growth measurements using multiple tracers of large-scale structure
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• Tension and constraints on modified gravity parametrizations of $G_{\text{eff}}(z)$ from growth rate and Planck data
• The VIMOS Public Extragalactic Redshift Survey (VIPERS): The growth of structures at $0.5<z<1.2$ from redshift-space distortions in the clustering of the PDR-2 final sample
• Local Gravity versus Local Velocity: Solutions for $\beta$ and nonlinear bias
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the full shape of the clustering wedges in the data release 10 and 11 galaxy samples
• The growth rate of cosmic structure from peculiar velocities at low and high redshifts
• Testing $\Lambda$CDM at the lowest redshifts with SN Ia and galaxy velocities
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: single-probe measurements from CMASS anisotropic galaxy clustering
• Is the Jeffreys' scale a reliable tool for Bayesian model comparison in cosmology?
• Observational constraints on Galileon cosmology
• On the evolution of density perturbations in f(R) theories of gravity
• Unification of Constant-roll Inflation and Dark Energy with Logarithmic $R^2$-corrected and Exponential $F(R)$ Gravity
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Observational constraints on viable f(R) parametrizations with geometrical and dynamical probes
• 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
• Constraining models of $f(R)$ gravity with Planck and WiggleZ power spectrum data
• Chameleon f(R) gravity in the virialized cluster
• Conjoined constraints on modified gravity from the expansion history and cosmic growth
• Large Scale Structure Constraints for a Class of f(R) Theories of Gravity
• Theoretical and observational constraints of viable f(R) theories of gravity
• Using dark energy to suppress power at small scales
• 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
• Can the degeneracies in the gravity sector be broken?

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• The Effective Fluid approach for Modified Gravity and its applications
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• Cosmological dynamics of f(R) models in dynamical system analysis
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• Viability of general relativity and modified gravity cosmologies using high-redshift cosmic probes
• Viability tests of \textit{f(R)}-gravity models with Supernovae Type 1A data
• Hypergeometric viable models in $f(R)$ gravity
• Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes
• Quasinormal Modes of Black holes in the generalized Schwarzschild-de Sitter solution of $f(R)$ gravity
• Observational constraints on a modified-gravity model with an exponential function of the curvature using the expansion history, the RSD, and the Pantheon+SH0ES data
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