Strong Bounds on Sum of Neutrino Masses in a 12 Parameter Extended Scenario with Non-Phantom Dynamical Dark Energy ($w(z)\geq -1$)

TL;DR

The paper investigates how strong bounds on the sum of active neutrino masses $\sum m_\nu$ survive in a 12-parameter extended cosmology that enforces non-phantom dynamical dark energy via the CPL form $w(z)=w_0+w_a(1-a)$. Using Planck 2015 data combined with BK14, BAO, Pantheon, Planck lensing, and a local $H_0$ prior from HST, the authors compare three models: NPDDE11+$r$ (with tensor modes), NPDDE11 (tensors off), and NPDDE11+$A_{\textrm{lens}}$ (varying lensing amplitude). They find the strongest bound $\sum m_\nu<0.123$ eV (95% CL) for Planck+BK14+BAO in the NPDDE11+$r$ model, with bounds weakening when $A_{\textrm{lens}}$ is allowed to vary; including HST generally pushes $N_{\rm eff}$ above the standard 3.045, hinting at mild dark radiation due to $H_0$ tension. In the $A_{\textrm{lens}}$-free case, $\sum m_\nu$ can still be constrained tightly, while the $A_{\textrm{lens}}$-varying case yields weaker neutrino bounds but better reconciliation of certain tensions (e.g., $\sigma_8$). These results demonstrate that precise neutrino-mass constraints persist even in high-dimensional models, and they underscore the nuanced interplay between dark-energy dynamics, lensing anomalies, and relativistic species content.

Abstract

We obtained constraints on a 12 parameter extended cosmological scenario including non-phantom dynamical dark energy (NPDDE) with CPL parametrization. We also include the six $Λ$CDM parameters, number of relativistic neutrino species ($N_{\textrm{eff}}$) and sum over active neutrino masses ($\sum m_ν$), tensor-to-scalar ratio ($r_{0.05}$), and running of the spectral index ($n_{run}$). We use CMB Data from Planck 2015; BAO Measurements from SDSS BOSS DR12, MGS, and 6dFS; SNe Ia Luminosity Distance measurements from the Pantheon Sample; CMB B-mode polarization data from BICEP2/Keck collaboration (BK14); Planck lensing data; and a prior on Hubble constant ($73.24\pm1.74$ km/sec/Mpc) from local measurements (HST). We have found strong bounds on the sum of the active neutrino masses. For instance, a strong bound of $\sum m_ν <$ 0.123 eV (95\% C.L.) comes from Planck+BK14+BAO. Although we are in such an extended parameter space, this bound is stronger than a bound of $\sum m_ν <$ 0.158 eV (95\% C.L.) obtained in $Λ\textrm{CDM}+\sum m_ν$ with Planck+BAO. Varying $A_{\textrm{lens}}$ instead of $r_{0.05}$ however leads to weaker bounds on $\sum m_ν$. Inclusion of the HST leads to the standard value of $N_{\textrm{eff}} = 3.045$ being discarded at more than 68\% C.L., which increases to 95\% C.L. when we vary $A_{\textrm{lens}}$ instead of $r_{0.05}$, implying a small preference for dark radiation, driven by the $H_0$ tension.

Figures (10)

• Figure 1: Comparison of 1-D marginalized posterior distributions for $\sum m_{\nu}$ (eV) and $N_\textrm{eff}$ for various data combinations in NPDDE11+$r$.
• Figure 2: 1$\sigma$ and 2$\sigma$ marginalized contours for $H_0$ (km/sec/Mpc) vs. $\sum m_{\nu}$ (eV) and $H_0$ (km/sec/Mpc) vs. $N_\textrm{eff}$ for Planck+BK14+HST in the NPDDE11+$r$ model, showing only a small correlation between $H_0$ and $\sum m_{\nu}$ whereas a strong positive correlation between $H_0$ vs. $N_\textrm{eff}$.
• Figure 3: 1$\sigma$ and 2$\sigma$ marginalized contours in the $\sigma_8-\Omega_m$ plane showing that the NPDDE+$r$ model is ineffective in reducing the tension between CFHTLenS and Planck 2015.
• Figure 4: Comparison of 1-D marginalized posterior distributions for $w_0$ and $w_a$ for different data combinations in NPDDE11+$r$.
• Figure 5: Comparison of 1-D marginalized posterior distributions for $\sum m_{\nu}$ (eV) and $N_\textrm{eff}$ for various data combinations in NPDDE11.