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Cosmological constraints on neutrinos after BICEP2

Jing-Fei Zhang, Yun-He Li, Xin Zhang

TL;DR

This work revisits the cosmology after BICEP2 by extending the base $\\Lambda$CDM+$r$ model to include neutrino-related parameters, analyzing four models that add $\\sum m_\\nu$, $N_{\\rm eff}$, both, or a massive sterile neutrino with $N_{\\rm eff}$ and $m_{\\nu,\\rm sterile}^{\\rm eff}$. Using Planck+WP+BAO in combination with $H_0$, SZ, lensing, cosmic shear, and BICEP2 data, the study finds that $\\sum m_\\nu$ is tightly constrained to $\\sim0.28$ eV when including $H_0$+SZ+Lensing (and remains around this value with BICEP2), providing strong evidence for nonzero active neutrino mass. $N_{\\rm eff}$ remains consistent with the standard value $3.046$ in most cases, though joint datasets that include BICEP2 indicate a mild preference for $\\Delta N_{\\rm eff}>0$ in certain models, especially those with $\\sum m_\\nu$. In the simultaneous $N_{\\rm eff}$ and $\\sum m_\\nu$ models and in the sterile-neutrino scenarios, the data favor nonzero masses and $\\Delta N_{\\rm eff}>0$ at high significance (up to ~4$\\sigma$ for active neutrinos and ~3.6$\\sigma$ for extra radiation), and the inclusion of sterile neutrinos can alleviate Planck–BICEP2 tension at the expense of elevating $n_s$ relative to a scale-invariant spectrum. Overall, the results illustrate the value of multi-dataset cosmology in constraining neutrino properties and in potentially reconciling tensions between CMB observations.

Abstract

Since the B-mode polarization of the cosmic microwave background (CMB) was detected by the BICEP2 experiment and an unexpectedly large tensor-to-scalar ratio, $r=0.20^{+0.07}_{-0.05}$, was found, the base standard cosmology should at least be extended to the 7-parameter $Λ$CDM+$r$ model. In this paper, we consider the extensions to this base $Λ$CDM+$r$ model by including additional base parameters relevant to neutrinos and/or other neutrino-like relativistic components. Four neutrino cosmological models are considered, i.e., the $Λ$CDM+$r$+$\sum m_ν$, $Λ$CDM+$r$+$N_{\rm eff}$, $Λ$CDM+$r$+$\sum m_ν$+$N_{\rm eff}$, and $Λ$CDM+$r$+$N_{\rm eff}$+$m_{ν,{\rm sterile}}^{\rm eff}$ models. We combine the current data, including 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, to constrain these neutrino cosmological models. We focus on the constraints on the parameters $\sum m_ν$, $N_{\rm eff}$, and $m_{ν,{\rm sterile}}^{\rm eff}$. We also discuss whether the tension on $r$ between Planck and BICEP2 can be relieved in these neutrino cosmological models.

Cosmological constraints on neutrinos after BICEP2

TL;DR

This work revisits the cosmology after BICEP2 by extending the base CDM+ model to include neutrino-related parameters, analyzing four models that add , , both, or a massive sterile neutrino with and . Using Planck+WP+BAO in combination with , SZ, lensing, cosmic shear, and BICEP2 data, the study finds that is tightly constrained to eV when including +SZ+Lensing (and remains around this value with BICEP2), providing strong evidence for nonzero active neutrino mass. remains consistent with the standard value in most cases, though joint datasets that include BICEP2 indicate a mild preference for in certain models, especially those with . In the simultaneous and models and in the sterile-neutrino scenarios, the data favor nonzero masses and at high significance (up to ~4 for active neutrinos and ~3.6 for extra radiation), and the inclusion of sterile neutrinos can alleviate Planck–BICEP2 tension at the expense of elevating relative to a scale-invariant spectrum. Overall, the results illustrate the value of multi-dataset cosmology in constraining neutrino properties and in potentially reconciling tensions between CMB observations.

Abstract

Since the B-mode polarization of the cosmic microwave background (CMB) was detected by the BICEP2 experiment and an unexpectedly large tensor-to-scalar ratio, , was found, the base standard cosmology should at least be extended to the 7-parameter CDM+ model. In this paper, we consider the extensions to this base CDM+ model by including additional base parameters relevant to neutrinos and/or other neutrino-like relativistic components. Four neutrino cosmological models are considered, i.e., the CDM++, CDM++, CDM+++, and CDM+++ models. We combine the current data, including 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, to constrain these neutrino cosmological models. We focus on the constraints on the parameters , , and . We also discuss whether the tension on between Planck and BICEP2 can be relieved in these neutrino cosmological models.

Paper Structure

This paper contains 10 sections, 13 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Models, parameters, and data
  3. Cosmological models involving neutrinos
  4. Observational data
  5. Results and discussions
  6. Constraints on the total mass of active neutrinos $\sum m_{\nu}$
  7. Constraints on the effective number of relativistic species $N_{\rm eff}$
  8. Simultaneous constraints on $N_{\rm eff}$ and $\sum m_{\nu}$
  9. Constraints on massive sterile neutrino with $N_{\rm eff}$ and $m_{\nu,{\rm sterile}}^{\rm eff}$
  10. Conclusion

Figures (4)

  • Figure 1: Cosmological constraints on the $\Lambda$CDM+$r$+$\sum m_\nu$ model.
  • Figure 2: Cosmological constraints on the $\Lambda$CDM+$r$+$N_{\rm eff}$ model.
  • Figure 3: Cosmological constraints on the $\Lambda$CDM+$r$+$\sum m_\nu$+$N_{\rm eff}$ model.
  • Figure 4: Cosmological constraints on the $\Lambda$CDM+$r$+$N_{\rm eff}$+$m_{\nu,{\rm sterile}}^{\rm eff}$ model.