Probing the neutrino mass hierarchy with CMB weak lensing

TL;DR

The paper assesses how future CMB experiments with weak-lensing reconstruction, notably a COrE-like mission, can determine the absolute neutrino mass scale and the mass hierarchy by combining primary CMB, lensing, and external geometric probes. Using MCMC forecasts with oscillation priors and Bayesian model selection, it finds that COrE alone could constrain $\sum m_ν$ to about $0.098$ eV (normal) or $0.136$ eV (inverted), and that including BAO, SNe (WFIRST), and a $2\%$ $H_0$ prior improves these to roughly $0.080$ eV and $0.118$ eV, with $w$ constrained to percent-level precision. The work shows that external geometrical data significantly boosts the ability to distinguish hierarchies—potentially around 12:1 odds in favor of the correct hierarchy for minimal-mass cases—though the evidence remains sensitive to the assumed priors and fiducial mass. It also finds that biases from assuming the wrong hierarchy are small, supporting Bayesian model averaging as a robust approach. Overall, the study demonstrates that CMB lensing together with oscillation priors and clean geometric data offers a promising path to resolving the neutrino mass ordering in the near future.

Abstract

We forecast constraints on cosmological parameters with primary CMB anisotropy information and weak lensing reconstruction with a future post-Planck CMB experiment, the Cosmic Origins Explorer (COrE), using oscillation data on the neutrino mass splittings as prior information. Our MCMC simulations in flat models with a non-evolving equation-of-state of dark energy w give typical 68% upper bounds on the total neutrino mass of 0.136 eV and 0.098 eV for the inverted and normal hierarchies respectively, assuming the total summed mass is close to the minimum allowed by the oscillation data for the respective hierarchies (0.10 eV and 0.06 eV). Including information from future baryon acoustic oscillation measurements with the complete BOSS, Type 1a supernovae distance moduli from WFIRST, and a realistic prior on the Hubble constant, these upper limits shrink to 0.118 eV and 0.080 eV for the inverted and normal hierarchies, respectively. Addition of these distance priors also yields percent-level constraints on w. We find tension between our MCMC results and the results of a Fisher matrix analysis, most likely due to a strong geometric degeneracy between the total neutrino mass, the Hubble constant, and w in the unlensed CMB power spectra. If the minimal-mass, normal hierarchy were realised in nature, the inverted hierarchy should be disfavoured by the full data combination at typically greater than the 2-sigma level. For the minimal-mass inverted hierarchy, we compute the Bayes' factor between the two hierarchies for various combinations of our forecast datasets, and find that the future probes considered here should be able to provide `strong' evidence (odds ratio 12:1) for the inverted hierarchy. Finally, we consider potential biases of the other cosmological parameters from assuming the wrong hierarchy and find that all biases on the parameters are below their 1-sigma marginalised errors.

Figures (13)

• Figure 1: Upper: Unlensed CMB temperature power spectra for a model with massless neutrinos (dashed red) and degenerate massive neutrinos with $\sum m_\nu = 0.37\,\mathrm{eV}$ (solid black). Both models are flat, have the same physical densities in cold dark matter and baryons, but different Hubble constants ($H_0 = 67.93\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ for the massive case and $H_0 = 71.43\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ for the massless case) to preserve the angular scale of the acoustic peaks. Lower: Fractional difference between the massive and massless model. Note that the $x$-axis is logarithmic for $l<50$ and linear for $l\geq 50$.
• Figure 2: Upper: Evolution of $p_{\mathrm{tot}}/\rho_{\mathrm{tot}}$ with scale factor $a$ for the massive (solid) and massless (dashed) models in Fig. \ref{['fig:Cls_mass_nmass']}. Lower: Difference between $p_{\mathrm{tot}}/\rho_{\mathrm{tot}}$ in these models. Also plotted are the relativistic approximation from equation (\ref{['eq:prho_rel']}) and the non-relativistic approximation from equation (\ref{['eq:prho_nonrel']}). The differences in $p_{\mathrm{tot}}/\rho_{\mathrm{tot}}$ at late times are due to the reduced energy density in dark energy in the massive model to preserve the angular scale of the CMB acoustic peaks.
• Figure 3: Upper: Fractional difference of the lensing power spectrum from a scenario with massless neutrinos, for a total mass of $0.095\,\mathrm{eV}$. The suppression of power on small scales is clearly seen. Lower: Fractional difference of the lensing power spectrum from a scenario with degenerate neutrinos, for a fixed total mass of 0.095 eV in the inverted hierarchy (blue) and normal hierarchy (green).
• Figure 4: Power spectrum of the statistical noise on lensing reconstructions for COrE using only temperature information (red) or temperature and polarization (blue). The linear-theory lensing deflection power spectrum is also shown (black), along with the effect of including the non-linear matter power spectrum (black dashed).
• Figure 5: Marginalised confidence regions (68 and 95 per cent) between the massive neutrino energy density and the rest of the parameter set for the inverted hierarchy. Shaded regions are MCMC results, and contours are from the Fisher matrix.