Matter Power Spectra in Viable $f(R)$ Gravity Models with Massive Neutrinos

Abstract

We investigate the matter power spectra in the power law and exponential types of viable $f(R)$ theories along with massive neutrinos. The enhancement of the matter power spectrum is found to be a generic feature in these models. In particular, we show that in the former type, such as the Starobinsky model, the spectrum is magnified much larger than the latter one, such as the exponential model. A greater scale of the total neutrino mass, $\Sigma m_{\nu }$, is allowed in the viable $f(R)$ models than that in the $\Lambda$CDM one. We obtain the constraints on the neutrino masses by using the CosmoMC package with the modified MGCAMB. Explicitly, we get $\Sigma m_{\nu }<0.451(0.214)\mathrm{eV}$ at 95% C.L. in the Starobinsky (exponential) model, while the corresponding one for the $\Lambda$CDM model is $\Sigma m_{\nu }<0.200\mathrm{eV}$. Furthermore, by treating the effective number of neutrino species $N_{\mathrm{eff}}$ as a free parameter along with $\Sigma m_{\nu }$, we find that $N_{\mathrm{eff}}=3.78_{-0.84}^{+0.64}(3.47_{-0.60}^{+0.74})$ and $\Sigma m_{\nu }=0.533_{-0.411}^{+0.254}$ ($<0.386)\mathrm{eV}$ at 95% C.L. in the Starobinsky (exponential) model.

15 pages, 5 figures, updated version accepted by PLB

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• Spatial Curvature in $f(R)$ Gravity
• Matter Power Spectra in Viable $f(R)$ Gravity Models with Dynamical Background
• Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory
• Cosmology based on $f(R)$ gravity with $\mathcal{O}(1)$ eV sterile neutrino
• Prospects for weighing neutrinos in interacting dark energy models using joint observations of gravitational waves and $\gamma$-ray bursts
• Large-scale structure power spectrum from scalar-tensor gravity
• Cosmological constraints on viable $f(R)$ models using weak lensing