Probing f (R) cosmology with sterile neutrinos via measurements of scale-dependent growth rate of structure

In this paper, we constrain the dimensionless Compton wavelength parameter B₀ of f (R) gravity as well as the mass of sterile neutrino by using the cosmic microwave background observations, the baryon acoustic oscillation surveys, and the linear growth rate measurements. Since both the f (R) model and the sterile neutrino generally predict scale-dependent growth rates, we utilize the growth rate data measured in different wavenumber bins with the theoretical growth rate approximatively scale-independent in each bin. The employed growth rate data come from the peculiar velocity measurements at z = 0 in five wavenumber bins, and the redshift space distortions measurements at z = 0.25 and z = 0.37 in one wavenumber bin. By constraining the f (R) model alone, we get a tight 95% upper limit of log₁₀ ⁡B₀ < - 4.1. This result is slightly weakened to log₁₀ ⁡B₀ < - 3.8 (at 2σ level) once we simultaneously constrain the f (R) model and the sterile neutrino mass, due to the degeneracy between the parameters of the two. For the massive sterile neutrino parameters, we get the effective sterile neutrino mass m_ν,sterile^eff < 0.62 eV (2σ) and the effective number of relativistic species N_eff < 3.90 (2σ) in the f (R) model. As a comparison, we also obtain m_ν,sterile^eff < 0.56 eV (2σ) and N_eff < 3.92 (2σ) in the standard ΛCDM model.