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

Abstract

In this paper, we constrain the dimensionless Compton wavelength parameter $B_0$ 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 ${\log }_{10}{B}_0<-4.1$. This result is slightly weakened to ${\log }_{10}{B}_0<-3.8$ (at 2$\sigma$ 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 $m_{\nu ,\mathrm{sterile}}^{\mathrm{eff}}<0.62$ eV (2$\sigma$) and the effective number of relativistic species $N_{\mathrm{eff}}<3.90$ (2$\sigma$) in the $f(R)$ model. As a comparison, we also obtain $m_{\nu ,\mathrm{sterile}}^{\mathrm{eff}}<0.56$ eV (2$\sigma$) and $N_{\mathrm{eff}}<3.92$ (2$\sigma$) in the standard $\Lambda$CDM model.

6 pages, 3 figures; revised version accepted for publication in Phys. Lett. B

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