Cluster-void degeneracy breaking: Neutrino properties and dark energy

Future large-scale spectroscopic astronomical surveys, e.g., Euclid, will enable the compilation of vast new catalogs of clusters and voids in the galaxy distribution. By combining the constraining power of both cluster and void number counts, such surveys could place stringent simultaneous limits on the sum of neutrino masses $M_{\nu }$ and the dark energy equation of state $w(z)=w_0+w_{a}z/(1+z)$. For minimal normal-hierarchy neutrino masses, we forecast that Euclid clusters+voids ideally could reach uncertainties $\sigma (M_{\nu })\lesssim 15\mathrm{meV}$, $\sigma (w_0)\lesssim 0.02$, $\sigma (w_a)\lesssim 0.07$, independent of other data. Such precision is competitive with expectations for, e.g., galaxy clustering and weak lensing in future cosmological surveys and could reject an inverted neutrino mass hierarchy at $\gtrsim 99\%$ confidence.

Figure 1

Forecast marginalized probability density functions (pdfs) for the summed neutrino mass $M_{\nu }$ from cluster and void abundances in the Euclid survey. A constant ($w_0$) or time-varying ($w_0$, $w_a$) dark energy equation of state is assumed. See Secs. 2 and 3 for definitions and details.

Figure 2

Forecast 68% parameter contours, and marginal probability density functions, from cluster and void abundances in future Euclid surveys. A dark energy equation of state $w(z)=w_0+w_{a}z/(1+z)$ is assumed. See Secs. 2 and 3 for definitions and details.

Figure 3

Void parameter sensitivity. We here use a generic void survey with $R_{\lim }=14h^{-1}\mathrm{Mpc}$ and $z=0.05–2.05,\mathrm{\Delta }{\log }_{10}(R/h^{-1}\mathrm{Mpc})=0.1,\mathrm{\Delta }z=0.2$. For each parameter, the figure shows $\mathrm{\Delta }{\chi }_{i,j}^{\mathrm{rel}}$ when that parameter only is varied. Hence, ${\sigma }_8$ is kept normalized to the fiducial value when other parameters are varied. See [5] for additional parameters. The turnover radius $R_{\mathrm{to}}(z)$ is shown in black, dotted lines. Scales related to the cosmological parameters are shown in brown, dotted lines ($k_{\mathrm{BAO}}=0.06h{\mathrm{Mpc}}^{-1}$, $k=0.05h{\mathrm{Mpc}}^{-1}$, $k_{\mathrm{FS}}^{\nu }\sim 0.003–0.05h{\mathrm{Mpc}}^{-1}$, $k_{\mathrm{eq}}=0.012h{\mathrm{Mpc}}^{-1}$). The coverage of the Euclid void surveys in terms of limiting radii and redshift is shown in red, dashed lines. See Sec. 4b for definitions and details.