Probing f(R)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 B0B0 of f(R)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)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=0z=0 in five wavenumber bins, and the redshift space distortions measurements at z=0.25z=0.25 and z=0.37z=0.37 in one wavenumber bin. By constraining the f(R)f(R) model alone, we get a tight 95% upper limit of log10⁡B0<−4.1log10⁡B0<−4.1. This result is slightly weakened to log10⁡B0<−3.8log10⁡B0<−3.8 (at 2σ   level) once we simultaneously constrain the f(R)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 mν,sterileeff<0.62 eV (2σ  ) and the effective number of relativistic species Neff<3.90Neff<3.90 (2σ  ) in the f(R)f(R) model. As a comparison, we also obtain mν,sterileeff<0.56 eV (2σ  ) and Neff<3.92Neff<3.92 (2σ) in the standard ΛCDM model.