Sweeping Horndeski Canvas: New Growth-Rate Parameterization for Modified-Gravity Theories

Abstract

We propose and numerically validate a new fitting formula that is sufficiently accurate to model the growth of structure in Horndeski theories of modified gravity for upcoming Stage IV and V large-scale structure surveys. Based on an analysis of more than 18,000 Horndeski models and adopting the popular parameterization of the growth rate $f(z)={\Omega }_M(z{)}^{\gamma }$, we generalize the constant growth index $\gamma$ to a two-parameter redshift-dependent quantity, $\gamma (z)$, that more accurately fits these models. We demonstrate that the functional form $\gamma (z)={\gamma }_0+{\gamma }_1{z}^2/(1+z)$ improves the median ${\chi }^2$ of the fit to viable Horndeski models by a factor of $\sim 40$ relative to that of a constant $\gamma$, and is sufficient to obtain unbiased results even for precise measurements expected in Stage IV and V surveys. Finally, we constrain the parameters of the new fitting formula using current cosmological data.

arXiv comment23 pages, 6 figures; prepared for JCAP submission; comments welcome! v2: Add missing footnote on author role on the first page; fix latex package rendering error in a section title. v3: Match the version accepted to JCAP; correct repeated references

References in corpus (75)

• Planck 2015 results. XIII. Cosmological parameters
• Efficient Computation of CMB anisotropies in closed FRW models
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant
• Exploring the Expansion History of the Universe
• 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
• Planck 2018 results. I. Overview and the cosmological legacy of Planck
• Chameleon Cosmology
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological Implications from two Decades of Spectroscopic Surveys at the Apache Point observatory
• The DESI Experiment Part I: Science,Targeting, and Survey Design
• Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• Cluster Abundance Constraints on Quintessence Models
• Cosmic Growth History and Expansion History
• Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)
• Quintessence: A Review
• Imperfect Dark Energy from Kinetic Gravity Braiding
• Horndeski theory and beyond: a review
• CMB power spectrum parameter degeneracies in the era of precision cosmology
• The 6dF Galaxy Survey: z \approx 0 measurement of the growth rate and sigma_8
• The Effective Field Theory of Dark Energy
• The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Anisotropic galaxy clustering in Fourier-space
• Dark Energy or Modified Gravity? An Effective Field Theory Approach
• The VIMOS Public Extragalactic Redshift Survey (VIPERS). Galaxy clustering and redshift-space distortions at z=0.8 in the first data release
• Cosmological solutions and growth index of matter perturbations in $f(Q)$ gravity
• 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 $z=0.15$
• The Clustering of Galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS): measuring growth rate and geometry with anisotropic clustering
• Cosmic flows in the nearby universe from Type Ia Supernovae
• Cosmology with Nonminimal Derivative Couplings
• 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
• Effective Field Theory of Cosmic Acceleration: an implementation in CAMB
• Gravitational Rainbows: LIGO and Dark Energy at its Cutoff
• Gravitational Lensing as a Probe of Quintessence
• 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
• Effective Field Theory of Dark Energy: a Review
• Dark Energy in light of Multi-Messenger Gravitational-Wave astronomy
• Effective Field Theory of Cosmic Acceleration: constraining dark energy with CMB data
• On the growth of linear perturbations
• Testing $\Lambda$CDM at the lowest redshifts with SN Ia and galaxy velocities
• A practical approach to cosmological perturbations in modified gravity
• Joint analysis of 6dFGS and SDSS peculiar velocities for the growth rate of cosmic structure and tests of gravity
• The growth of matter perturbations in f(R) models
• The Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) Survey Design, Reductions, and Detections
• The 6dF Galaxy Velocity Survey: Cosmological constraints from the velocity power spectrum
• Cosmic flows in the nearby Universe: new peculiar velocities from SNe and cosmological constraints
• Growth factor parametrization and modified gravity
• Cosmological parameter constraints for Horndeski scalar-tensor gravity
• Evidence for suppression of structure growth in the concordance cosmological model
• Reconstructing Gravity on Cosmological Scales
• The Taipan Galaxy Survey: Scientific Goals and Observing Strategy
• Cosmological Constraints on Horndeski Gravity in Light of GW170817
• A parametrization of the growth index of matter perturbations in various Dark Energy models and observational prospects using a Euclid-like survey
• Is the Effective Field Theory of Dark Energy Effective?
• An Extended action for the effective field theory of dark energy: a stability analysis and a complete guide to the mapping at the basis of EFTCAMB
• Linear growth in power law $f(T)$ gravity
• The road ahead of Horndeski: cosmology of surviving scalar-tensor theories
• Searching for Modified Gravity: Scale and Redshift Dependent Constraints from Galaxy Peculiar Velocities
• New Gravitational Scales in Cosmological Surveys
• Testing deviations from $\Lambda$CDM with growth rate measurements from 6 Large Scale Structure Surveys at $\mathbf{z}=0.06$ to 1
• Linear growth index of matter perturbations in Rastall gravity
• A parametrization for the growth index of linear matter perturbations
• A local measurement of the growth rate from peculiar velocities and galaxy clustering correlations in the 6dF Galaxy Survey
• Growth index with the exact analytic solution of sub-horizon scale linear perturbation for dark energy models with constant equation of state
• Planck ISW-lensing likelihood and the CMB temperature
• An Accurate Fitting Function For Scale-dependent Growth Rate in Hu-Sawicki $f(R)$ Gravity
• Imprints of interacting dark energy on cosmological perturbations
• Growth index of matter perturbations in the light of Dark Energy Survey
• Cosmological Probes of Structure Growth and Tests of Gravity
• The End of Cosmic Growth
• Global properties of the growth index: mathematical aspects and physical relevance

Cited by in corpus (9)

• Underdetermination of dark energy
• Matching current observational constraints with nonminimally coupled dark energy
• How much information can be extracted from galaxy clustering at the field level?
• Modified gravity and massive neutrinos: constraints from the full shape analysis of BOSS galaxies and forecasts for Stage IV surveys
• Compressed baryon acoustic oscillation analysis is robust to modified-gravity models
• The SRG/eROSITA All-Sky Survey : Constraints on the structure growth from cluster number counts
• Exploring the Growth Index ${\gamma }_L$: Insights from Different CMB Dataset Combinations and Approaches
• Reconstructing the growth index $\gamma$ with Gaussian Processes
• Principal Components for Model-Agnostic Modified Gravity with 3x2pt