Analytic solution for matter density perturbations in a class of viable cosmological f(R) models

Abstract

For a class of viable cosmological models in $f(R)$ gravity which deviation from the Einstein gravity decreases as a inverse power law of the Ricci scalar $R$ for large $R$, an analytic solution for density perturbations in the matter component during the matter dominated stage is obtained in terms of hypergeometric functions. An analytical expression for the matter transfer function at scales much less than the present Hubble scale is also obtained.

11 pages; More discussion and references added, results unchanged, matches the version to be published in IJMPD; A typo in eq. (25) is fixed

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• Density perturbations in general modified gravitational theories
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• Cosmology Based on f(R) Gravity Admits 1 eV Sterile Neutrinos
• Phantom boundary crossing and anomalous growth index of fluctuations in viable f(R) models of cosmic acceleration
• Consistency relation for $R^p$ inflation
• Large Scale Structure Constraints for a Class of f(R) Theories of Gravity
• Stability analysis for cosmological models in $f(R)$ gravity using dynamical system analysis
• Constraints on f(R) theory and Galileons from the latest data of galaxy redshift surveys
• Dark energy: investigation and modeling
• Constraint on the cosmological f(R) model from the multipole power spectrum of the SDSS luminous red galaxy sample and prospects for a future redshift survey
• Cosmic acceleration from modified gravity with Palatini formalism
• Future Oscillations around Phantom Divide in f(R) Gravity
• Reheating after f(R) inflation
• Black hole perturbation in parity violating gravitational theories
• f(R) Gravity and its Cosmological Implications
• Constraint on reheating after f(R) inflation from gravitational waves
• Characterizing the linear growth rate of cosmological density perturbations in an f(R) model
• Matter power spectrum in f(R) gravity with massive neutrinos
• Black hole perturbation in nondynamical and dynamical Chern-Simons gravity
• Testing Modified Gravity with Cosmic Shear
• Jeans Instability in Classical and Modified Gravity
• Observational constraints on Starobinsky $f(R)$ cosmology from cosmic expansion and structure growth data
• Parameterizing scalar-tensor theories for cosmological probes
• Linear growth of matter density perturbations in f(R,G) theories
• $f(R)$ gravity: scalar perturbations in the late Universe
• What is the amplitude of the Gravitational Waves background expected in the Starobinsky model ?
• Density perturbations in $f(R,\varphi )$-gravity with an application to the (varying power)-law model
• A new approach to cosmological perturbations in f(R) models
• Complete density perturbations in the Jordan-Fierz-Brans-Dicke theory
• Covariant gauge invariant theory of Scalar Perturbations in $f(R)$-gravity: a brief review
• Gravitational instability in oscillating background
• Numerical analysis of the generalized Starobinsky inflationary model
• Viability of general relativity and modified gravity cosmologies using high-redshift cosmic probes
• Density perturbation and cosmological evolution in the presence of magnetic field in $f(R)$ gravity models