Neutrinos in the holographic dark energy model: constraints from latest measurements of expansion history and growth of structure

The model of holographic dark energy (HDE) with massive neutrinos and/or dark radiation is investigated in detail. The background and perturbation evolutions in the HDE model are calculated. We employ the PPF approach to overcome the gravity instability difficulty (perturbation divergence of dark energy) led by the equation-of-state parameter $w$ evolving across the phantom divide $w=-1$ in the HDE model with $c<1$. We thus derive the evolutions of density perturbations of various components and metric fluctuations in the HDE model. The impacts of massive neutrino and dark radiation on the CMB anisotropy power spectrum and the matter power spectrum in the HDE scenario are discussed. Furthermore, we constrain the models of HDE with massive neutrinos and/or dark radiation by using the latest measurements of expansion history and growth of structure, including the Planck CMB temperature data, the baryon acoustic oscillation data, the JLA supernova data, the Hubble constant direct measurement, the cosmic shear data of weak lensing, the Planck CMB lensing data, and the redshift space distortions data. We find that $sum m_ u<0.186$ eV (95% CL) and $N_{rm eff}=3.75^{+0.28}_{-0.32}$ in the HDE model from the constraints of these data.

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 $B_0$ 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 $m_{ u,{rm{sterile}}}^{rm{eff}}<0.62$ eV (2$sigma$) and the effective number of relativistic species $N_{rm eff}<3.90$ (2$sigma$) in the $f(R)$ model. As a comparison, we also obtain $m_{ u,{rm{sterile}}}^{rm{eff}}<0.56$ eV (2$sigma$) and $N_{rm eff}<3.92$ (2$sigma$) in the standard $Lambda$CDM model.