Implications of $f(R)$ gravity on late-time cosmic structure growth through a complete description of density perturbations

Abstract

We provide insight about the full form of the equations for matter density perturbations and the scalar Bardeen metric potentials in general $f(R)$ theories of gravity. When considering viable modifications to the standard $\Lambda$CDM background, the full scale-dependent equations for the metric perturbations are provided and are shown to match the ones obtained with the quasistatic approximation. We investigate the impact of the $n=2$ Hu-Sawicki model on the late-time growth of structures. We find that updated late-time growth of structure data imposes $|f_{R_0}|\lesssim 10^{-6}-10^{-5}$ and thus conclude that the Hu-Sawicki $f(R)$ model contributes no significant phenomenology at both background and perturbative level beyond the effective cosmological constant encompassed in its definition. This conclusion points to the survival of the present tension between early and late measurements of ${\sigma }_8$, as the Hu-Sawicki model can only worsen this issue or at best reproduce the results from the current concordance cosmological model. The generalized perturbative method showcased in this work can be applied to more elaborate $f(R)$ models to isolate genuine higher-order signatures beyond the quasistatic approximation.

arXiv comment20 pages, 8 figures, Matches published version in Physics of the Dark Universe

References in corpus (53)

• f(R) theories
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• Quintessence, Cosmic Coincidence, and the Cosmological Constant
• An alternative to quintessence
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Generalized Chaplygin Gas, Accelerated Expansion and Dark Energy-Matter Unification
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• f(T) teleparallel gravity and cosmology
• Disappearing cosmological constant in f(R) gravity
• DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations
• Massive neutrinos and cosmology
• Cosmology and Fundamental Physics with the Euclid Satellite
• Extra force in $f(R)$ modified theories of gravity
• Unification of Dark Matter and Dark Energy: the Inhomogeneous Chaplygin Gas
• The Pantheon+ Analysis: The Full Dataset and Light-Curve Release
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Cobaya: Code for Bayesian Analysis of hierarchical physical models
• Quintessence: A Review
• Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?
• Accelerating universe from F(T) gravity
• First evidence that non-metricity f(Q) gravity could challenge $\Lambda$CDM
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Black Holes in f(R) theories
• 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
• The realistic models of relativistic stars in f(R) = R + alpha R^2 gravity
• The 6dF Galaxy Survey: Peculiar Velocity Field and Cosmography
• Gravitational collapse in f(R) theories
• New constraints on $f(R)$ gravity from clusters of galaxies
• On the evolution of density perturbations in f(R) theories of gravity
• Supernovae and the Nature of the Dark Energy
• New observational constraints on $f(R)$ gravity from cosmic chronometers
• The Pantheon+ Analysis: Improving the Redshifts and Peculiar Velocities of Type Ia Supernovae Used in Cosmological Analyses
• The VIMOS Public Extragalactic Redshift Survey (VIPERS). Gravity test from the combination of redshift-space distortions and galaxy-galaxy lensing at $0.5<z<1.2$
• Internal Robustness of Growth Rate data
• FLRW solutions in $f(Q)$ theory: the effect of using different connections
• Unraveling the effective fluid approach for $f(R)$ models in the subhorizon approximation
• Ultra-light axions and the $S_8$ tension: joint constraints from the cosmic microwave background and galaxy clustering
• Tension of the $E_G$ statistic and RSD data with Planck/$\Lambda$CDM and implications for weakening gravity
• Mapping the Real Space Distributions of Galaxies in SDSS DR7: II. Measuring the growth rate, clustering amplitude of matter and biases of galaxies at redshift $0.1$
• Reconstructing the inflationary $f(R)$ from observations
• Theoretical and observational constraints of viable f(R) theories of gravity
• Is cosmography a useful tool for testing cosmology?
• A Step in Understanding the $S_8$ Tension
• Optimising growth of structure constraints on modified gravity
• Accuracy of environmental tracers and consequence for determining the Type Ia Supernovae magnitude step
• The Integrated Sachs-Wolfe Effect in Interacting Dark Energy Models
• Cosmological constraints on non-adiabatic dark energy perturbations
• An Accurate Fitting Function For Scale-dependent Growth Rate in Hu-Sawicki $f(R)$ Gravity
• Hubble tension in a nonminimally coupled curvature-matter gravity model
• Is cosmological data suggesting a nonminimal coupling between matter and gravity?
• Exploring the inflation of $F(R)$ gravity
• Constraining viscous fluid models in $f(Q)$ gravity with data

Cited by in corpus (1)

• Cosmological and lunar laser ranging constraints on evolving dark energy in a nonminimally coupled curvature-matter gravity model