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.

23 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 (19)

• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• 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
• The DESI Experiment Part I: Science,Targeting, and Survey Design
• Imperfect Dark Energy from Kinetic Gravity Braiding
• Horndeski theory and beyond: a review
• 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
• 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 $z=0.15$
• Effective Field Theory of Cosmic Acceleration: constraining dark energy with CMB data
• On the growth of linear perturbations
• Joint analysis of 6dFGS and SDSS peculiar velocities for the growth rate of cosmic structure and tests of gravity
• The 6dF Galaxy Velocity Survey: Cosmological constraints from the velocity power spectrum
• Growth factor parametrization and modified gravity
• New Gravitational Scales in Cosmological Surveys
• A local measurement of the growth rate from peculiar velocities and galaxy clustering correlations in the 6dF Galaxy Survey
• Planck ISW-lensing likelihood and the CMB temperature
• Imprints of interacting dark energy on cosmological perturbations
• Cosmological Probes of Structure Growth and Tests of Gravity

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• 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