Unraveling the effective fluid approach for $f(R)$ models in the subhorizon approximation

Abstract

We provide explicit formulas for the effective fluid approach of $f(R)$ theories, such as the Hu & Sawicki and the designer models. Using the latter and simple modifications to the CLASS code, which we call EFCLASS, in conjunction with very accurate analytic approximations for the background evolution, we obtain competitive results in a much simpler and less error-prone approach. We also derive the initial conditions in matter domination and we find they differ from those already found in the literature for a constant $w$ model. A clear example is the designer model that behaves as $\Lambda$CDM in the background, but has nonetheless dark energy perturbations. We then use the aforementioned models to derive constraints from the latest cosmological data, including supernovae, BAO, CMB, $H(z)$ and growth-rate data, and find they are statistically consistent to the $\Lambda$CDM model. Finally, we show that the viscosity parameter $c_{vis}^2$ in realistic models is not constant as commonly assumed, but rather evolves significantly over several orders of magnitude, something which could affect forecasts of upcoming surveys.

24 pages, 12 figures, 5 tables. Changes match published version. The codes used in the analysis can be found at https://members.ift.uam-csic.es/savvas.nesseris/efclass.html and https://github.com/wilmarcardonac/EFCLASS

References in corpus (57)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Bayes in the sky: Bayesian inference and model selection in cosmology
• Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2
• Dark Energy after GW170817: dead ends and the road ahead
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Baryon Acoustic Oscillations in the Lyα forest of BOSS DR11 quasars
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• The Large Scale Structure of f(R) Gravity
• A Parameterized Post-Friedmann Framework for Modified Gravity
• Measuring the dark side (with weak lensing)
• Distinguishing Modified Gravity from Dark Energy
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Testing cosmological structure formation using redshift-space distortions
• 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 $z=0.15$
• Searching for modified growth patterns with tomographic surveys
• Dark Energy: the equation of state description versus scalar-tensor or modified gravity
• Cosmology and Astrophysical Constraints of Gauss-Bonnet Dark Energy
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• Anisotropic stress as signature of non-standard propagation of gravitational waves
• A f(R) gravity without cosmological constant
• Testing gravity with CAMB and CosmoMC
• Dark Energy versus Modified Gravity
• Gauss-Bonnet Quintessence: Background Evolution, Large Scale Structure and Cosmological Constraints
• Current constraints on the cosmic growth history
• Galileon Gravity in Light of ISW, CMB, BAO and $H_0$ data
• How to optimally parametrize deviations from General Relativity in the evolution of cosmological perturbations
• Observables and unobservables in dark energy cosmologies
• Cosmological perfect-fluids in f(R) gravity
• On the evolution of density perturbations in f(R) theories of gravity
• Constraints on a New Post-General Relativity Cosmological Parameter
• Constraining Dark Energy Anisotropic Stress
• Measuring the Speed of Dark: Detecting Dark Energy Perturbations
• Growth rate of cosmological perturbations at z ~ 0.1 from a new observational test
• Energy Conditions and Cosmic Acceleration
• The phenomenological approach to modeling the dark energy
• A new perspective on Dark Energy modeling via Genetic Algorithms
• Fingerprinting dark energy
• Measuring the speed of cosmological gravitational waves
• Effects of modified gravity on B-mode polarization
• Confronting General Relativity with Further Cosmological Data
• A comparison of Einstein-Boltzmann solvers for testing General Relativity
• Cosmological constraints and comparison of viable $f(R)$ models
• Bayesian Evidence against Harrison-Zel'dovich spectrum in tension cosmology
• Anisotropic stress and stability in modified gravity models
• Testing Einstein's gravity and dark energy with growth of matter perturbations: Indications for new Physics?
• Consistency of Modified Gravity with a decreasing $G_{\mathrm{eff}}(z)$ in a $\Lambda$CDM background
• Clustering dark energy and halo abundances
• The WiggleZ Dark Energy Survey: constraining the evolution of Newton's constant using the growth rate of structure
• The End of Cosmic Growth

Cited by in corpus (57)

• A $w-M$ phantom transition at $z_t<0.1$ as a resolution of the Hubble tension
• Hubble tension or a transition of the Cepheid SnIa calibrator parameters?
• Hints of a Local Matter Underdensity or Modified Gravity in the Low $z$ Pantheon data
• What can Machine Learning tell us about the background expansion of the Universe?
• Tension of the $E_G$ statistic and RSD data with Planck/$\Lambda$CDM and implications for weakening gravity
• Observational constraints on the deceleration parameter in a tilted universe
• Scalar induced gravitational waves from primordial black hole Poisson fluctuations in $f(R)$ gravity
• Measurements of $H_0$ and reconstruction of the dark energy properties from a model-independent joint analysis
• Model independent calibrations of gamma ray bursts using machine learning
• Novel null tests for the spatial curvature and homogeneity of the Universe and their machine learning reconstructions
• Constraints on the distance duality relation with standard sirens
• Kinematic constraints beyond $z\simeq 0$ using calibrated GRB correlations
• Designing Horndeski and the effective fluid approach
• Cosmological constraints of phantom dark energy models
• Hints of dark energy anisotropic stress using Machine Learning
• Constraints on the transition redshift from the calibrated Gamma-ray Burst $E_{\mathrm{p}}$-$E_{\mathrm{iso}}$ correlation
• Machine learning constraints on deviations from general relativity from the large scale structure of the Universe
• The Hubble Tension, The $M$ Crisis of Late Time $H(z)$ Deformation Models and the Reconstruction of Quintessence Lagrangians
• Gravitational wave propagation in $f(R)$ models: New parametrizations and observational constraints
• Cosmological Constraints on sub-horizon scales modified gravity theories with MGCLASS II
• Machine Learning meets the redshift evolution of the CMB Temperature
• Constraining power of cosmological observables: blind redshift spots and optimal ranges
• New late-time constraints on $f(R)$ gravity
• Cosmological constraints on non-adiabatic dark energy perturbations
• Equivalence between Horndeski and beyond Horndeski theories and imperfect fluids
• Spatial Curvature in $f(R)$ Gravity
• Can $f(R)$ gravity relieve $H_0$ and ${\sigma }_8$ tensions?
• Machine Learning and cosmographic reconstructions of quintessence and the Swampland conjectures
• Dark energy reconstructions combining BAO data with galaxy clusters and intermediate redshift catalogs
• Testing the $\Lambda$CDM paradigm with growth rate data and machine learning
• Forecast constraints on Anisotropic Stress in Dark Energy using gravitational-waves
• Constraints from observational data for a running cosmological constant and warm dark matter with curvature
• Is gravity getting weaker at low z? Observational evidence and theoretical implications
• Dark sector evolution in Horndeski models
• Cosmology in Brans-Dicke-de Rham-Gabadadze-Tolley massive gravity
• Constraints on Cosmographic Functions of Cosmic Chronometers Data Using Gaussian Processes
• The Effective Fluid approach for Modified Gravity and its applications
• Breaking the baryon-dark matter degeneracy in a model-independent way through the Sunyaev-Zeldovich effect
• Cosmological constraints with the Effective Fluid approach for Modified Gravity
• Machine learning unveils the linear matter power spectrum of modified gravity
• Stress testing the dark energy equation of state imprint on supernova data
• Tracking the validity of the quasi-static and sub-horizon approximations in modified gravity
• Lower tensor-to-scalar ratio as possible signature of modified gravity
• Explaining JWST star formation history at $z\sim 17$ by modifying $\Lambda$CDM
• Constraints on the minimally extended varying speed of light model using the Pantheon+ dataset
• Scrutinizing coupled vector dark energy in light of data
• Effects of Dark Energy anisotropic stress on the matter power spectrum
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• $\Lambda CDM$ periodic cosmology
• Characterizing the equivalence between dark energy and radiation using gamma-ray bursts
• Determining $H_0$ from distance sum rule combining gamma-ray bursts with observational Hubble data and strong gravitational lensing
• Lensing convergence and anisotropic dark energy in galaxy redshift surveys
• Implications of $f(R)$ gravity on late-time cosmic structure growth through a complete description of density perturbations
• Model independent reconstruction of cosmological accelerated-decelerated phase
• Probing dynamical embeddings in a five-dimensional spacetime in light of DESI BAO
• Intermediate redshift calibration of Gamma-ray Bursts and cosmic constraints in non-flat cosmology
• An effective fluid description of scalar-vector-tensor theories under the sub-horizon and quasi-static approximations