Cosmic constraint on massive neutrinos in viable f(R) gravity with producing LCDM background expansion

TL;DR

This work assesses whether a viable $f(R)$ gravity model that recreates a $\\Lambda$CDM background can host massive neutrinos to address cosmological tensions in $H_0$ and $\\sigma_8$. By performing a joint analysis of Planck 2015 CMB data with RSD, BAO, and JLA SN, plus an $H_0$ prior, the authors constrain both active and sterile neutrino masses and the gravity-sector parameter $f_{R0}$ within the viable $f(R)$ framework. They obtain upper limits $\\Sigma m_\\nu < 0.202$ eV and $m_{\\nu, eff}^{sterile} < 0.757$ eV with $N_{eff} < 3.22$, along with corresponding lower bounds on $f_{R0}\\times 10^{-6}$, namely $>-1.89$ (active) and $>-2.02$ (sterile). The derived cosmological parameters indicate neutrino properties notably influence $z_{eq}$, $k_{eq}$, $100\\theta_{s,eq}$, and $Y_p$, and the $H_0$ tension is mildly reduced compared to standard $\\Lambda$CDM. Overall, the study shows that viable modified gravity models can be consistent with current data while imprinting neutrino physics on cosmic evolution.

Abstract

Tensions between several cosmic observations were found recently, such as the inconsistent values of $H_{0}$ (or $σ_{8}$) were indicated by the different cosmic observations. Introducing the massive neutrinos in $Λ$CDM could potentially solve the tensions. Viable $f(R)$ gravity producing $Λ$CDM background expansion with massive neutrinos is investigated in this paper. We fit the current observational data: Planck-2015 CMB, RSD, BAO and SNIa to constrain the mass of neutrinos in viable $f(R)$ theory. The constraint results at 95\% confidence level are: $Σm_ν<0.202$ eV for the active neutrino case, $m_{ν, sterile}^{eff}<0.757$ eV with $N_{eff}<3.22$ for the sterile neutrino case. For the effects by the mass of neutrinos, the constraint results on model parameter at 95\% confidence level become $f_{R0}\times 10^{-6}> -1.89$ and $f_{R0}\times 10^{-6}> -2.02$ for two cases, respectively. It is also shown that the fitting values of several parameters much depend on the neutrino properties, such as the cold dark matter density, the cosmological quantities at matter-radiation equality, the neutrino density and the fraction of baryonic mass in helium. At last, the constraint result shows that the tension between direct and CMB measurements of $H_0$ gets slightly weaker in the viable $f(R)$ model than that in the base $Λ$CDM model.

Figures (4)

• Figure 1: The contours of model parameters in viable $f(R)$ theory with massive neutrino by fitting the Planck TT, TE, EE+lowP and the low-redshift data: Planck lesning+RSD+BAO+JLA.
• Figure 2: The $1-D$ distributions of basic cosmological parameters in viable $f(R)$ model with massive neutrino.
• Figure 3: The $1-D$ distributions of derived cosmological parameters in viable $f(R)$ model with massive neutrino.
• Figure 4: The values of $f\sigma_{8}$ calculated in the viable $f(R)$ model with the massive neutrino, where blue line denotes the active-neutrino case, and red line denotes the sterile-neutrino case. Ten dots with error bar denote the observational datapoints from Refs. RSD1RSD2RSD3RSD4RSD5RSD6