Constraining neutrino properties with a Euclid-like galaxy cluster survey

TL;DR

This work forecasts the neutrino physics reach of a Euclid-like photometric cluster survey by combining cluster number counts and cluster power spectrum within an MCMC framework and in synergy with Planck CMB data. It analyzes a baseline $\Lambda$CDM+$m_\nu$ model and extensions including $N_{\text{eff}}$, a non-zero $w$, and non-zero curvature, along with a self-calibration treatment of the mass–observable relation. The main finding is that Planck+Euclid can constrain the total neutrino mass to $\sum m_\nu<0.031$ eV (95% CL), with a potential $2\sigma$ detection even in the normal hierarchy, while $N_{\text{eff}}$ can be constrained to $<3.14$ (95% CL); allowing extra parameters slightly weakens these bounds. When nuisance parameters are marginalized with no priors, the constraints degrade significantly (e.g., $\sum m_\nu<0.083$ eV), underscoring the importance of robust calibration of the mass–richness relation, particularly via Euclid's weak-lensing measurements. Overall, the results demonstrate strong synergy between optical/near-IR cluster surveys and CMB data in constraining neutrino properties and the growth of structure, provided mass calibration is well controlled.

Abstract

We perform a forecast analysis on how well a Euclid-like photometric galaxy cluster survey will constrain the total neutrino mass and effective number of neutrino species. We base our analysis on the Monte Carlo Markov Chains technique by combining information from cluster number counts and cluster power spectrum. We find that combining cluster data with CMB measurements from Planck improves by more than an order of magnitude the constraint on neutrino masses compared to each probe used independently. For the LCDM+m_nu model the 2 sigma upper limit on total neutrino mass shifts from M_nu < 0.35 eV using cluster data alone to M_nu < 0.031 eV when combined with CMB data. When a non-standard model with N_eff number of neutrino species is considered, we estimate N_eff<3.14 (95% CL), while the bounds on neutrino mass are relaxed to M_nu < 0.040 eV. This accuracy would be sufficient for a 2 sigma detection of neutrino mass even in the minimal normal hierarchy scenario. We also consider scenarios with a constant dark energy equation of state and a non-vanishing curvature. When these models are considered the error on M_nu is only slightly affected, while there is a larger impact of the order of ~ 15 % and ~ 20% respectively on the 2 sigma error bar of N_eff with respect to the standard case. We also treat the LCDM+m_nu+N_eff case with free nuisance parameters, which parameterize the uncertainties on the cluster mass determination. In this case, the upper bounds on M_nu are relaxed by a factor larger than two, M_nu < 0.083 eV (95% CL), hence compromising the possibility of detecting the total neutrino mass with good significance. We thus confirm the potential that a large optical/near-IR cluster survey, like that to be carried out by Euclid, could have in constraining neutrino properties [abridged].

Figures (9)

• Figure 1: Effects of the variation of $\sum m_\nu$ and $N_{\text{eff}}$ on the linear matter power spectrum (left) and halo mass function (right) at $z=0$; all other parameters $(\Omega_{\rm m}, \Omega_\Lambda, H_0, n_{\rm s}, \Delta^2_{\rm R}, \tau)$ are kept fixed to the WMAP 9-yr best-fit values for $\Lambda$CDM. See text for comments.
• Figure 2: Wavenumber dependence of the relative error of the cluster power spectrum, $\sigma_{\bar{P}^{cl}}/\bar{P}^{cl}$ defined as in Eq. \ref{['eqn:sigp']}, at four different redshift: $z=0.2, 0.6, 1.0, 1.6$, from bottom to top curves, respectively.
• Figure 3: The cumulative cluster redshift distribution as predicted by the reference cosmological model and the reference values for the mass nuisance parameters (see Table 1), for the Euclid cluster survey.
• Figure 4: The $68\%$ and $95\%$ CL contours in the $(\sum m_\nu$-$\sigma_8)$ plane for a $\Lambda$CDM+$m_\nu$ model. Left panel: contours from cluster power spectrum (large contours; $P^{cl}$-only) and the combination of cluster power spectrum and number counts (small contours; Euclid-Cl). The insert plot shows a zoom of the confidence contours given by the Euclid-Cl dataset compared with the contours obtained from the Fisher Matrix technique using the same dataset. Right panel: contours from Planck (green), Euclid-Cl (red) and Planck+Euclid-Cl (blue) datasets. The insert plot shows a zoom of the confidence contours obtained from the Planck+Euclid-Cl datasets.
• Figure 5: The $68\%$ and $95\%$ CL contours in the $\sum m_\nu-(\Omega_{\rm m},n_{\rm s})$ planes for a $\Lambda$CDM+$m_\nu$ model, from Euclid-Cl (red contours) and the Planck+Euclid-Cl (blue contours) datasets. When only Euclid-Cl dataset is used the parameter $\tau$, which is not constrained by this data, is kept fixed to its fiducial value $0.085$.