Accurately weighing neutrinos with cosmological surveys

A promising avenue to measure the total, and potentially individual, mass of neutrinos consists of leveraging cosmological datasets, such as the cosmic microwave background and surveys of the large-scale structure of the Universe. In order to obtain unbiased estimates of the neutrino mass, however, many effects ought to be included. Here we forecast, via a Markov chain Monte Carlo likelihood analysis, whether measurements by two galaxy surveys, DESI and Euclid, when added to the CMB-S4 experiment, are sensitive to two effects that can alter neutrino-mass measurements. The first is the slight difference in the suppression of matter fluctuations that each neutrino-mass hierarchy generates at fixed total mass. The second is the growth-induced scale-dependent bias of haloes produced by massive neutrinos. We find that near-future surveys can distinguish hierarchies with the same total mass only at the $1\sigma$ level; thus, while these are poised to deliver a measurement of the sum of neutrino masses, they cannot significantly discern the mass of each individual neutrino in the foreseeable future. We further find that neglecting the growth-induced scale-dependent bias induces up to a $1\sigma$ overestimation of the total neutrino mass, and we show how to absorb this effect via a redshift-dependent parametrization of the scale-independent bias.

Figure 1

Percent differences in $\mathrm{CDM}+\mathrm{baryon}$ power spectra compared to a massless neutrino cosmology: for different total neutrino masses assuming the degenerate hierarchy (upper panel) and for different hierarchies assuming a total neutrino mass of 100 meV (lower panel). In each case we fix the cosmological parameters $\{{\omega }_b,{\omega }_{\mathrm{cdm}},{\mathrm{\Omega }}_m,A_s,n_s\}$, varying $h$. As shown, the primary effect of massive neutrinos is a suppression of amplitude at small scales—the change in amplitude at large scales is attributed to varying values of $h$. Note that both the total mass and individual neutrino masses affect the amount of suppression and scale at which it turns on, though the latter effect is subdominant. In addition, the amount of suppression is redshift dependent, with a larger spread at small scales for larger neutrino masses.

Figure 2

The GISDB for redshifts from 0.65 (lightest) to 1.65 (darkest) with massive neutrinos. The total neutrino mass is set at 90 meV and the degenerate scenario is assumed. As shown, the GISDB is both scale and redshift dependent.

Figure 3

Percent differences in galaxy power spectra ${\tilde{P}}_g(k,z,\mu )$ between the various neutrino hierarchies (at fixed $\sum m_{\nu }=100\mathrm{meV}$), as well as with and without the GISDB, compared to a fiducial case of inverted hierarchy with GISDB, at $z=0.75$. The shot noises associated with DESI and Euclid are shown as the shaded areas. Here the cosmological parameters $\{{\omega }_b,{\omega }_{\mathrm{cdm}},h,A_s,n_s,\sum m_{\nu }\}$ as well as all bias and RSD nuisance parameters are held fixed.

Figure 4

MCMC Posteriors for $h$, ${\tau }_{\mathrm{reio}}$, and $\sum m_{\nu }$ for CMB-S4 and various LSS experiments. For each, the fiducial cosmology has an Inverted hierarchy in the minimum-mass configuration, with total neutrino mass 98 meV.

Figure 5

Posteriors for $\mathrm{CMB}\text{−}\mathrm{S}4+\mathrm{Euclid}$ with a prior on ${\tau }_{\mathrm{reio}}$ with a width of 0.01, assuming degenerate hierarchy with and without GISDB, and assuming the IH with total neutrino mass 98 meV as fiducial.