Constraint on f(R) Gravity through the Redshift Space Distortion

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In this paper, a specific family of f(R) models that can produce the ΛCDM background expansion history is constrained by using the currently available geometric and dynamic probes. The scale dependence of the growth rate f(z,k) in this specific family of f(R) model is shown. Therefore to eliminate the scale dependence of fσ₈(z) in theory, which usually is defined as the product of f(z,k) and σ₈(z), we define fσ₈(z)=dσ₈(z)/d a which is obviously scale independent and reproduces the conventional definition in the standard ΛCDM cosmology. In doing so, under the assumption that future probes having the same best fit values as the current ten data points of fσ₈(z), even having 20% error bars enlarged, we find a preliminary constraint fᵣ₀=-2.58₋₀.₅₈⁺².¹⁴× 10⁻⁶ in 1σ regions. This indicates the great potential that redshift space distortions have in constraining modified gravity theories. We also discuss the nonlinear matter power spectrum based on different halo fit models.