Measuring neutrino masses with a future galaxy survey

TL;DR

This work forecasts the neutrino-mass sensitivity of a Euclid-like photometric survey combined with Planck CMB data, using both galaxy clustering and cosmic shear angular power spectra. The authors model full two-point statistics $C^{XY}_{\ell,ij}$, incorporate measurement and systematic errors, and generate mock data with redshift tomography and scale-dependent bias treatment, analyzed via nested sampling. They find that the sum of neutrino masses $\sum m_\nu$ can be detected at $1.5$–$2.5\sigma$ under conservative assumptions, rising to $\sim5.4\sigma$ with perfect knowledge of galaxy bias; the joint shear+galaxy data are crucial for breaking degeneracies with $\omega_m$ and $H_0$ and achieving these sensitivities. Even with extended cosmological parameters ($N_{\rm eff}^{ml}$, $w$) and bias marginalisation, the combined data remain highly constraining, though they cannot resolve the neutrino mass hierarchy; the results emphasize the powerful complementarity of Euclid’s shear and galaxy probes for precision neutrino cosmology.

Abstract

We perform a detailed forecast on how well a Euclid-like photometric galaxy and cosmic shear survey will be able to constrain the absolute neutrino mass scale. Adopting conservative assumptions about the survey specifications and assuming complete ignorance of the galaxy bias, we estimate that the minimum mass sum of sum m_nu ~ 0.06 eV in the normal hierarchy can be detected at 1.5 sigma to 2.5 sigma significance, depending on the model complexity, using a combination of galaxy and cosmic shear power spectrum measurements in conjunction with CMB temperature and polarisation observations from Planck. With better knowledge of the galaxy bias, the significance of the detection could potentially reach 5.4 sigma. Interestingly, neither Planck+shear nor Planck+galaxy alone can achieve this level of sensitivity; it is the combined effect of galaxy and cosmic shear power spectrum measurements that breaks the persistent degeneracies between the neutrino mass, the physical matter density, and the Hubble parameter. Notwithstanding this remarkable sensitivity to sum m_nu, Euclid-like shear and galaxy data will not be sensitive to the exact mass spectrum of the neutrino sector; no significant bias (< 1 sigma) in the parameter estimation is induced by fitting inaccurate models of the neutrino mass splittings to the mock data, nor does the goodness-of-fit of these models suffer any significant degradation relative to the true one (Delta chi_eff ^2< 1).

Figures (12)

• Figure 1: Angular power spectra for three redshift bins (bin 1: $z \in [0,0.61]$, bin 2: $z\in [0.61,1.03]$, bin 3: $z \in [1.03,3]$). Thick solid lines are the bin-autocorrelation spectra, thin solid lines bin-cross-correlations, both include HaloFit nonlinear corrections. The corresponding linear theory spectra are plotted as dashed lines. Top: cosmic shear angular power spectra. Bottom: galaxy angular power spectra. At low multipoles $\ell$, the galaxy signals in different redshift bins are anticorrelated. The $(1,3)$-cross-spectrum is strongly suppressed because the corresponding bins are not adjoining, and is therefore not shown in the plot.
• Figure 2: Angular shear-galaxy cross-power spectra for two identical redshift bins in shear and galaxies (bin 1: $z \in [0,0.61]$, bin 2: $z\in [0.61,1.03]$). The first number denotes the index of the shear redshift bin, the second the index of the galaxy bin. Note that unlike the ss and gg bin-cross-correlations, the sg cross-correlations are not symmetric in the redshift bin indices. Solid lines include HaloFit nonlinear corrections, while dashed lines are the corresponding linear theory spectra.
• Figure 3: Two examples illustrating our redshift binning scheme and the corresponding redshift-dependent $\ell_{\rm max}^{\rm g}$ for mock galaxy data. Black lines denote eight redshift bins, while red lines represent a two-bin scheme. Solid lines correspond to $\epsilon_{\rm nl} = 1$, and dashed lines represent the linear-only case with $\epsilon_{\rm nl} = 0.1$. Also plotted in gold is the differential source galaxy surface density from equation (\ref{['eq:galdist']}), with an arbitrary normalisation.
• Figure 4: Standard deviation of the marginalised posterior distribution for $\omega_{\mathrm dm}$ ( top left), $h$ ( top right) and $\sum m_\nu$ ( bottom), derived for various combinations of synthetic Planck CMB data and Euclid data. Red:Planck+shear auto-spectrum. Black/Grey:Planck+galaxy auto-spectrum without/with marginalisation over $N_{\rm bin}$ bias parameters. Dotted lines denote galaxy data on linear scales only ($\epsilon_{\rm nl}=0.1$), while solid lines include data on mildly nonlinear scales ($\epsilon_{\rm nl} = 1$).
• Figure 5: Forecast two-dimensional joint marginalised 68%- and 95%-credible contours in the $(\omega_{\rm m},h,\sum m_\nu)$-subspace. Black:Planck CMB data+galaxy auto-spectrum (11 bins) without bias marginalisation. Red:Planck CMB+shear auto-spectrum (2 bins). Green:Planck+galaxy auto-spectrum+shear auto-spectrum+shear-galaxy cross-correlation.