Weighing neutrinos in the scenario of vacuum energy interacting with cold dark matter: application of the parameterized post-Friedmann approach

TL;DR

This paper investigates how vacuum energy interacting with cold dark matter impacts cosmological neutrino mass constraints by applying the parameterized post-Friedmann ($PPF$) framework to two IDE forms, $Q=\beta H\rho_{\rm c}$ and $Q=\beta H\rho_{\Lambda}$. Using Planck CMB data plus BAO/SNIa/H0 and LSS observations, it finds $\beta>0$ at >1σ for the $Q=\beta H\rho_{\rm c}$ model, indicating CDM decay into vacuum energy, while $\beta=0$ is consistent for the $Q=\beta H\rho_{\Lambda}$ model. Relative to $\Lambda$CDM, the inferred upper bounds on the total neutrino mass are $\sum m_\nu<0.11$ eV (2σ) in the base model (with DR12 BAO and $H_0=73.00\pm1.75$ km s$^{-1}$ Mpc$^{-1}$), $\sum m_\nu<0.20$ eV (2σ) for $Q=\beta H\rho_{\rm c}$, and $\sum m_\nu<0.10$ eV (2σ) or $<0.14$ eV (2σ) for $Q=\beta H\rho_{\Lambda}$ depending on data combinations. The results reveal that shifts in neutrino-mass limits are influenced by the $H_0$ tension with other data and that the PPF approach stabilizes perturbations across IDE scenarios, enabling robust neutrino weighing in extended cosmologies.

Abstract

We constrain the neutrino mass in the scenario of vacuum energy interacting with cold dark matter by using current cosmological observations. To avoid the large-scale instability problem in interacting dark energy models, we employ the parameterized post-Friedmann (PPF) approach to do the calculation of perturbation evolution, for the $Q=βHρ_{\rm c}$ and $Q=βHρ_Λ$ models. The current observational data sets used in this work include Planck (cosmic microwave background), BSH (baryon acoustic oscillations, type Ia supernovae, and Hubble constant), and LSS (redshift space distortions and weak lensing). According to the constraint results, we find that $β>0$ at more than $1σ$ level for the $Q=βHρ_{\rm c}$ model, which indicates that cold dark matter decays into vacuum energy; while $β=0$ is consistent with the current data at $1σ$ level for the $Q=βHρ_Λ$ model. Taking the $Λ$CDM model as a baseline model, we find that a smaller upper limit, $\sum m_ν<0.11$ eV ($2σ$), is induced by the latest BAO BOSS DR12 data and the Hubble constant measurement $H_{0} = 73.00 \pm 1.75$ km~s$^{-1}$~Mpc$^{-1}$. For the $Q=βHρ_{\rm c}$ model, we obtain $\sum m_ν<0.20$ eV ($2σ$) from Planck+BSH. For the $Q=βHρ_Λ$ model, $\sum m_ν<0.10$ eV ($2σ$) and $\sum m_ν<0.14$ eV ($2σ$) are derived from Planck+BSH and Planck+BSH+LSS, respectively. We show that these smaller upper limits on $\sum m_ν$ are affected more or less by the tension between $H_{0}$ and other observational data.

Figures (6)

• Figure 1: One-dimensional marginalized distributions and two-dimensional contours at $1\sigma$ and $2\sigma$ level for parameters $\sum m_{\nu}$, $\Omega_{\rm m}$, and $H_{0}$ of the $\Lambda$CDM+$\sum m_{\nu}$ model by using Planck+BSH.
• Figure 2: The one-dimensional posterior distributions for the coupling parameter $\beta$ in the $Q=\beta H \rho_{\rm c}$ (left) and $Q=\beta H \rho_{\Lambda}$ (right) models, with fixed neutrino mass $\sum m_\nu=0.06$ eV.
• Figure 3: The two-dimensional marginalized contours ($1\sigma$ and $2\sigma$) in the $\beta$--$\Omega_{\rm m}$ and $\beta$--$H_0$ planes for the $Q=\beta H \rho_{\rm c}$ model (with fixed neutrino mass $\sum m_\nu=0.06$ eV) by using Planck+BSH.
• Figure 4: One-dimensional marginalized distributions and two-dimensional contours at $1\sigma$ and $2\sigma$ levels for parameters $\beta$, $\sum m_{\nu}$, $\Omega_{\rm m}$, and $H_{0}$ of the $Q=\beta H \rho_{\rm c}$ model in the presence of $\sum m_{\nu}$ by using Planck+BSH.
• Figure 5: The two-dimensional marginalized contours ($1\sigma$ and $2\sigma$) in the $\beta$--$\Omega_{\rm m}$ and $\beta$--$H_0$ planes for the $Q=\beta H \rho_{\Lambda}$ model (with fixed neutrino mass $\sum m_\nu=0.06$ eV) by using Planck+BSH and Planck+BSH+LSS.