Galaxy clustering, CMB and supernova data constraints on $φ$CDM model with massive neutrinos

TL;DR

This study tests a dynamical dark energy model $φ$CDM with an inverse-power-law potential $V(φ) ∝ φ^{-α}$ in the presence of massive neutrinos, examining how $Σm_ν$ and $α$ shape the CMB and matter power spectra. Using a joint data set of Planck 2013, WMAP9, WiggleZ, BOSS DR11, and the JLA SN sample, the authors constrain the model parameters with MCMC. They find $α<4.995$ (95% CL) and $Σm_ν<0.262$ eV (95% CL) for $φ$CDM, with ΛCDM ($α=0$) still allowed, and show that increasing $α$ or $Σm_ν$ suppresses the matter power spectrum, implying a degeneracy that favors smaller $Σm_ν$ when $α$ is large. The results indicate that current data tighten bounds on dynamical dark energy and neutrino masses but do not decisively distinguish between a time-varying dark energy component and a cosmological constant, though the allowed neutrino mass scale is marginally smaller in $φ$CDM than in ΛCDM.

Abstract

We investigate a scalar field dark energy model (i.e., $φ$CDM model) with massive neutrinos, where the scalar field possesses an inverse power-law potential, i.e., $V(φ)\propto φ^{-α}$ ($α>0$). We find that the sum of neutrino masses $Σm_ν$ has significant impacts on the CMB temperature power spectrum and on the matter power spectrum. In addition, the parameter $α$ also has slight impacts on the spectra. A joint sample, including CMB data from Planck 2013 and WMAP9, galaxy clustering data from WiggleZ and BOSS DR11, and JLA compilation of Type Ia supernova observations, is adopted to confine the parameters. Within the context of the $φ$CDM model under consideration, the joint sample determines the cosmological parameters to high precision. It turns out that $α<4.995$ at 95% CL for the $φ$CDM model. And yet, the $Λ$CDM scenario corresponding to $α= 0$ is not ruled out at 95% CL. Moreover, we get $Σm_ν< 0.262$ eV at 95% CL for the $φ$CDM model, while the corresponding one for the $Λ$CDM model is $Σm_ν < 0.293$ eV. The allowed scale of $Σm_ν$ in the $φ$CDM model is a bit smaller than that in the $Λ$CDM model. It is consistent with the qualitative analysis, which reveals that the increases of $α$ and $Σm_ν$ both can result in the suppression of the matter power spectrum. As a consequence, when $α$ is larger, in order to avoid suppressing the matter power spectrum too much, the value of $Σm_ν$ should be smaller.

Figures (4)

• Figure 1: Impacts of the sum of neutrino masses $\Sigma m_{\nu}$ on the matter power spectrum $P(k)$ and on the CMB temperature power spectrum $C_l^{TT}$ in the $\phi$CDM (upper panels) and $\Lambda$CDM (lower panels) models. $\Sigma m_{\nu}$ is varied, and other parameters are kept fixed.
• Figure 2: Impacts of the parameter $\alpha$ on the matter power spectrum $P(k)$ and on the CMB temperature power spectrum $C_l^{TT}$ in the framework of $\phi$CDM model. $\alpha$ is varied, and other parameters are kept fixed.
• Figure 3: The 1D and 2D probability distributions of parameters of interest in the $\Lambda$CDM model constrained with the joint sample. In the 1D plots, the solid lines denote the marginalized likelihoods and the dotted lines correspond to the mean likelihoods. In the 2D plots, the contours refer to the marginalized likelihoods while the colors refer to the mean likelihoods. The contours correspond to 68%, 95% and 99% confidence levels.
• Figure 4: The 1D marginalized distribution and 2D contours of parameters of interest in the $\phi$CDM model constrained from the joint sample. The implications of line styles and colors are the same as those in Fig. \ref{['fig:LCDM_contour']}.