Constraining Neutrino Masses by CMB Experiments Alone

TL;DR

This work demonstrates that cosmological constraints on neutrino masses can be derived from CMB data alone within a ΛCDM framework with adiabatic perturbations, yielding a 95% CL bound of $\sum m_{\nu} < 2.0$ eV (degenerate case $m_{\nu}<0.66$ eV) under flatness, and showing robustness to moderate curvature. The authors develop and utilize reduced CMB observables $\ell_1$, $H_1$, $H_2$, and $H_3$ to interpret how neutrino mass, via free streaming and the early ISW effect, shifts the acoustic peak structure, and they provide analytic insights linking $\omega_{\nu}$ to these observables. A meticulous χ^2-minimization approach with a large ensemble of CMB templates demonstrates that nonzero $\omega_{\nu}$ raises the minimum $\chi^2$, yielding the upper limit $\omega_{\nu}<0.021$ (=$m_{\nu}<0.66$ eV). Allowing non-flat geometry leaves the limit essentially unchanged, though curvature can affect the inferred Hubble constant and tighten the bound in extreme cases. The results underscore the value and limits of CMB-only neutrino-mass constraints and highlight that substantial improvements require external priors on $H_0$ or complementary data.

Abstract

It is shown that a subelectronvolt upper limit can be derived on the neutrino mass from the CMB data alone in the Lambda CDM model with the power-law adiabatic perturbations, without the aid of any other cosmological data. Assuming the flatness of the universe, the constraint we can derive from the current WMAP observations is \sum m_nu < 2.0 eV at the 95% confidence level for the sum over three species of neutrinos (m_nu < 0.66 eV for the degenerate neutrinos). This constraint modifies little even if we abandon the flatness assumption for the spatial curvature. We argue that it would be difficult to improve the limit much beyond \sum m_nu \lesssim 1.5 eV using only the CMB data, even if their statistics are substantially improved. However, a significant improvement of the limit is possible if an external input is introduced that constrains the Hubble constant from below. The parameter correlation and the mechanism of CMB perturbations that give rise to the limit on the neutrino mass are also elucidated.

Figures (12)

• Figure 1: Minimum $\chi^2$ as a function of the neutrino energy density $\omega_{\nu}$. The solid curve is for the flat universe. The dotted and the dashed curves show the cases for a negative and a positive curvature universe, respectively.
• Figure 2: The cosmological parameters for the solutions that give minimum $\chi^2$ as a function of $\omega_{\nu}$. The two line segmants shown in panel (c) are the cases for a negative (dotted line) and a positive (dashed line) curvature universe.
• Figure 3: The values of reduced CMB observables for the solutions that give minimum $\chi^2$ as a function of $\omega_{\nu}$.
• Figure 4: Constraints on the four reduced CMB observables. Local $\chi^2$ is computed using restricted sets of multipoles as explained in the text and is measured with $\chi^2_{\rm local}$ in the relevant range indicated in the left ordinate. The $\chi^2$ of global solution is measured for the value with respect to the entire data set as measured in the right ordinate. The relative normalisation is fixed so that the global solution that gives $\chi^2$ minimum gives the local $\chi^2$ value measured in the left ordinate. Dotted curves are the envelopes for $\omega_\nu=0.01$, 0.02 and 0.03 in the order of increasing minimum $\chi^2$. The horizontal dashed line segments show the position of $\chi^2-\chi^2_{\rm min}=4$.
• Figure 5: Response of the four reduced CMB observables to the variation of $\omega_{\nu}$. The isolated points show the values at $\omega_\nu=0$, which do not connect to the $\omega_\nu\ne 0$ values smoothly.