Detecting neutrino mass difference with cosmology

TL;DR

This work questions the common cosmological assumption of degenerate neutrino masses in light of terrestrial mass-squared splittings, notably $|\Delta m^2_{23}|\sim2.5\times10^{-3}\ \mathrm{eV}^2$. It extends prior analyses by modeling two neutrino masses ($m_1=m_2$ and $m_3=\alpha\sum m_i$) and including CMB lensing reconstruction, evaluating impacts on the CMB, matter, and lensing spectra via CAMB and Fisher-matrix methods. The findings show that for realistic neutrino masses, non-degeneracy corrections are below current numerical accuracy for CMB and matter, with lensing only revealing potential biases in ideal experiments; however, degeneracies with other parameters prevent a direct detection of the mass difference. In exotic scenarios without tight splitting constraints, non-degeneracy could produce substantial corrections across probes, underscoring that the degeneracy assumption is generally robust but not universally valid. Overall, lensing remains the most promising avenue to probe mass differences, but breaking parameter degeneracies is crucial for a definitive measurement.

Abstract

Cosmological parameter estimation exercises usually make the approximation that the three standard neutrinos have degenerate mass, which is at odds with recent terrestrial measurements of the difference in the square of neutrino masses. In this paper we examine whether the use of this approximation is justified for the cosmic microwave background (CMB) spectrum, matter power spectrum and the CMB lensing potential power spectrum. We find that, assuming m^2_{23} ~ 2.5x10^{-3}$eV^2 in agreement with recent Earth based measurements of atmospheric neutrino oscillations, the correction due to non-degeneracy is of the order of precision of present numerical codes and undetectable for the foreseeable future for the CMB and matter power spectra. An ambitious experiment that could reconstruct the lensing potential power spectrum to the cosmic variance limit up to l~1000 will have to take the effect into account in order to avoid biases. The degeneracies with other parameters, however, will make the detection of the neutrino mass difference impossible. We also show that relaxing the bound on the neutrino mass difference will also increase the error-bar on the sum of neutrino masses by a factor of up to a few. For exotic models with significantly non-degenerate neutrinos the corrections due to non-degeneracy could become important for all the cosmological probes discussed here.

Figures (4)

• Figure 1: The lensed CMB power spectrum (top), the matter power spectrum (middle) and the lensing potential power spectrum (bottom). Solid line correspond to the standard $\Lambda$CDM model. Other two models plotted have $\sum m_i=2$eV and $\alpha=1/3$ (dotted) or $\alpha=1$ (dashed). See text for discussion.
• Figure 2: This figure shows the change in the $\chi^2$ for a cosmic variance limited experiment (to $\ell=2000$) if one wrongly assumes degenerate neutrinos. The contours are at $\Delta \chi^2$ of 1, 5, 25 and 125 (from $\alpha=1/3$ line outwards). See text for discussion of other features on the plot.
• Figure 3: Same as Figure \ref{['fig:cl']} but for the lensing potential reconstruction that is cosmic variance up to $\ell=1000$.
• Figure 4: This figure shows the relative change in the matter power spectrum slope at $k=0.005 h/$Mpc (top), $0.01 h/$Mpc (middle) and $0.1 h/$Mpc (bottom). The thin solid and dotted lines correspond to 0.1% (dotted), 1% and 10% difference and increase in value from the thin horizontal dashed line outwards.