Neutrinos and dark energy after Planck and BICEP2: data consistency tests and cosmological parameter constraints

TL;DR

This work addresses the tension between BICEP2's detection of primordial gravitational waves and Planck-era cosmology by extending the base model to a dynamical dark energy framework with constant w, alongside four neutrino/dark-radiation variants. Using a combination of Planck, WMAP, BAO, H0, SZ cluster counts, CMB lensing, cosmic shear, and BICEP2 data, the authors test data consistency before deriving joint constraints on the dark energy equation of state, total neutrino mass, Neff, and sterile-neutrino mass. The analysis shows that sterile neutrinos plus dynamical dark energy provide the strongest cross-dataset consistency, significantly relaxing tensions among CMB, H0, cluster counts, and lensing with BICEP2. These results highlight the importance of including light sterile neutrinos and non-constant dark energy behavior in interpreting current cosmological data and set the stage for tighter constraints with future observations.

Abstract

The detection of the B-mode polarization of the cosmic microwave background (CMB) by the BICEP2 experiment implies that the tensor-to-scalar ratio $r$ should be involved in the base standard cosmology. In this paper, we extend the $Λ$CDM+$r$+neutrino/dark radiation models by replacing the cosmological constant with the dynamical dark energy with constant $w$. Four neutrino plus dark energy models are considered, i.e., the $w$CDM+$r+\sum m_ν$, $w$CDM+r + $N_{\rm eff}$, $w$CDM+r + $\sum m_ν$ + $N_{\rm eff}$, and $w$CDM+r + $N_{\rm eff}$ + $m_{ν,{\rm sterile}}^{\rm eff}$ models. The current observational data considered in this paper include the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data, the cosmic shear data, and the BICEP2 polarization data. We test the data consistency in the four cosmological models, and then combine the consistent data sets to perform joint constraints on the models. We focus on the constraints on the parameters $w$, $\sum m_ν$, $N_{\rm eff}$, and $m_{ν,{\rm sterile}}^{\rm eff}$.

Figures (8)

• Figure 1: The Planck+WP+BAO constraints in the $\Omega_m$--$H_0$, $\Omega_m$--$\sigma_8$, and $n_s$--$r_{0.002}$ planes for the $\Lambda$CDM/$w$CDM+$r$+$\sum m_\nu$ models (first-row panels), the $\Lambda$CDM/$w$CDM+$r$+$N_{\rm eff}$ models (second-row panels), the $\Lambda$CDM/$w$CDM+$r$+$\sum m_\nu$+$N_{\rm eff}$ models (third-row panels), and the $\Lambda$CDM/$w$CDM+$r$+$N_{\rm eff}$+$m_{\nu,{\rm sterile}}^{\rm eff}$ models (fourth-row panels). The gray bands stand for the observational results, i.e., the HST result of Hubble constant $H_0=73.8\pm 2.4$ km s$^{-1}$ Mpc$^{-1}$h0, the Planck result of SZ cluster counts $\sigma_8(\Omega_m/0.27)^{0.3}=0.782\pm 0.010$SZ, and the BICEP2 result of tensor-to-scalar ratio $r=0.20^{+0.07}_{-0.05}$bicep2.
• Figure 2: One-dimensional posterior distributions for the $w$CDM+$r$+$\sum m_\nu$ model (upper) and the $w$CDM+$r$+$N_{\rm eff}$ model (lower).
• Figure 3: Two-dimensional joint, marginalized constraints for the $w$CDM+$r$+$\sum m_\nu$+$N_{\rm eff}$ model (upper) and the $w$CDM+$r$+$N_{\rm eff}$+$m_{\nu,{\rm sterile}}^{\rm eff}$ model (lower).
• Figure 4: Two-dimensional joint, marginalized constraints in the $r_{0.002}-n_s$ plane for the four models.
• Figure 5: Cosmological constraints on the $w$CDM+$r$+$\sum m_\nu$ model.