Constraints on non-flat cosmologies with massive neutrinos after Planck 2015

TL;DR

This paper investigates how the total neutrino mass $\Sigma m_{\nu}$ and spatial curvature constrain two dark-energy frameworks, ΛCDM and φCDM with an inverse power-law potential $V(\phi) \propto \phi^{-\alpha}$ ($\alpha>0$), under two neutrino-mass hierarchies (degenerate vs heaviest-dominant) in both flat and non-flat universes. It performs a joint analysis of Planck 2015 CMB data, BAO measurements, JLA SNe, and $H_0$ priors using CosmoMC across four models (P1–P4) and two hierarchies. The results show tight bounds on $\Sigma m_{\nu}$ in the flat case, e.g., $\Sigma m_{\nu} < 0.165$ eV (ΛCDM) and $<0.164$ eV (φCDM) for Scenario I, with significantly weaker limits when curvature is allowed (non-flat: $<0.299$ eV and $<0.301$ eV); in Scenario II the flat bounds are $<0.166$ eV and $<0.164$ eV while non-flat bounds are $<0.354$ eV and $<0.364$ eV. Differences between hierarchies are small in the flat case but more pronounced in the non-flat case, and the constraints are similar for ΛCDM and φCDM at a fixed hierarchy. Overall, current data impose strong neutrino-mass limits but reveal a notable degeneracy with spatial curvature, limiting the ability to distinguish dark-energy dynamics from a cosmological constant.

Abstract

We investigate two dark energy cosmological models (i.e., the $Λ$CDM and $φ$CDM models) with massive neutrinos assuming two different neutrino mass hierarchies in both the spatially flat and non-flat scenarios, where in the $φ$CDM model the scalar field possesses an inverse power-law potential, $V(φ)\propto φ^{-α}$ ($α>0$). Cosmic microwave background data from Planck 2015, baryon acoustic oscillations data from 6dFGS, SDSS-MGS, BOSS-LOWZ and BOSS CMASS-DR11, the JLA compilation of Type Ia supernova apparent magnitude observations, and the Hubble Space Telescope $H_0$ prior, are jointly employed to constrain the model parameters. We first determine constraints assuming three species of degenerate massive neutrinos. In the spatially flat (non-flat) $Λ$CDM model, the sum of neutrino masses is bounded as $Σm_ν < 0.165 (0.299)$ eV at 95% confidence level (CL). Correspondingly, in the flat (non-flat) $φ$CDM model, we find $Σm_ν < 0.164 (0.301)$ eV at 95% CL. The inclusion of spatial curvature as a free parameter results in a significant broadening of confidence regions for $Σm_ν$ and other parameters. In the scenario where the total neutrino mass is dominated by the heaviest neutrino mass eigenstate, we can obtain the similar conclusions as those obtained in the degenerate neutrino mass scenario. In addition, the results show that the bounds on $Σm_ν$ based on two different neutrino mass hierarchies have insignificant differences in the spatially flat case for both the $Λ$CDM and $φ$CDM models, however, the corresponding differences are larger in the non-flat case.

Figures (3)

• Figure 2: Contours refer to the marginalized likelihoods at 68% and 95% confidence levels constrained from the joint analysis using the HST $H_0$ prior for the $\Lambda$CDM model in the scenario assuming three species of degenerate massive neutrinos. Left and middle panels: contours in the $(\Omega_m, \Sigma m_{ })$ and $( _8, \Sigma m_{ })$ planes, where the thin blue (thick red) lines correspond to constraints in the flat (non-flat) scenario. The "+" ("x") marks the mean values of the pair in the flat (non-flat) scenario. Right panel: contours in the $(\Omega_k, \Sigma m_{ })$ plane for the non-flat scenario. The "x" marks the mean values of the $(\Omega_k, \Sigma m_{ })$ pair.
• Figure 3: Contours refer to the marginalized likelihoods at 68% and 95% confidence levels constrained from the joint analysis using the HST $H_0$ prior for the $$CDM model in the scenario assuming three species of degenerate massive neutrinos. Upper left, upper right and lower left panels: contours in the $(\Omega_m, \Sigma m_{ })$, $( _8, \Sigma m_{ })$ and $( , \Sigma m_{ })$ planes, where the thin blue (thick red) lines correspond to constraints in the flat (non-flat) scenario. The "+" ("x") marks the mean values of the pair in the flat (non-flat) scenario. Lower right panel: contours in the $(\Omega_k, \Sigma m_{ })$ plane for the non-flat scenario. The "x" marks the mean values of the $(\Omega_k, \Sigma m_{ })$ pair.
• Figure 4: Contours refer to the marginalized likelihoods at 68% and 95% confidence levels in the non-flat $\Lambda$CDM model assuming three species of degenerate massive neutrinos constrained from the joint sample with two different $H_0$ priors. From left to right, contours in the $(\Omega_m, \Sigma m_{ })$, $( _8, \Sigma m_{ })$ and $(\Omega_k, \Sigma m_{ })$ planes are presented, respectively. The thin black lines correspond to constraints from the joint sample with the $H_0 = (68 \pm 2.8)$ km s$^{-1}$ Mpc$^{-1}$ prior from Chen & Ratra (2011). The thick red lines correspond to constraints from the joint sample with the $H_0 = (73.8\pm 2.4)$ km s$^{-1}$ Mpc$^{-1}$ (Riess et al. 2011) prior from HST observations. The "+" marks the mean values of the corresponding pair with $H_0$ prior from Chen & Ratra (2011). The "x" marks the mean values with $H_0$ prior from Riess et al. (2011).