The imprints of massive neutrinos on the 3-point correlation function of large-scale structures

Abstract

Free-streaming of cosmic neutrinos impacts the distribution and growth of cosmic structures on small scales, allowing constraints on the sum of neutrino masses $M_ν$ from clustering studies. In this work, we investigate for the first time the possibility of disentangling massive neutrino cosmologies with the 3-point correlation function (3PCF). We measure the isotropic connected 3PCF $ζ$ and the reduced 3PCF $Q$ of halo catalogues from the Quijote suite of N-body simulations, considering $M_ν=0.0, 0.1, 0.2,$ and $0.4 \, \mathrm{eV}$ in different redshift bins. We develop a framework to quantify the detectability of massive neutrinos for different triangle configurations and shapes, and apply it to a case compatible with a Stage-IV spectroscopic survey. We also compare our results with the analysis of simulations without neutrinos, but with different $σ_8$ values, to test whether the 3PCF can break the well-known degeneracy between the two parameters. We find that, as a result of free-streaming, the largest signal is found for quasi-isosceles and squeezed triangles; this signal is increasing for decreasing redshifts. Among these configurations, elongated triangles, tracing the filamentary structure of the cosmic web, are the most affected by the impact of massive neutrinos, with a 3PCF signal increasing with $M_ν$. A complementary source of signal comes from right-angled triangles in $Q$. Importantly, we find that the signatures of a $σ_8$ variation appear significantly different on elongated triangles in $ζ$ and right-angled triangles in $Q$, suggesting that the 3PCF can be used to effectively break the $M_ν- σ_8$ degeneracy. These results open the possibility to use the 3PCF as a powerful complementary tool to constrain neutrino masses in current and future spectroscopic surveys like DESI, Euclid, 4MOST, and the Nancy Grace Roman Space Telescope.

Figures (11)

• Figure 1: The values of the parameter $\tilde{\chi}^2(s_{12}, s_{13})$ defined in Eq. \ref{['eq:single-scale_chi_det']}, for the single-scale connected 3PCF, obtained for $M_\nu = 0.4$ eV. Each panel corresponds to a different redshift: from left to right, $z = 0, 1$, and 2. The lines overplotted on the left panel are taken as representative of regions of enhanced signal, and identify isosceles triangles (black dashed line with $\eta = 0$, where the signal is enhanced only on scales $\lesssim 30$$h^{-1}$ Mpc), quasi-isosceles triangles with $\eta = 4$ (green dashed line), and triangles with $s_{12} = 10$$h^{-1}$ Mpc (blue dash-dotted line). The numbered circles on the lines identify some ($s_{12}, s_{13}$) configurations, corresponding, in increasing order from 1 to 4, to (10,100), (30,100), (55,100), and (30,50) $h^{-1}$ Mpc. For them, we plot the single-scale $\zeta$ in Fig. \ref{['fig:single_scales_zeta']}.
• Figure 2: Single-scale connected 3PCF for the triangle configurations selected in Fig. \ref{['fig:single_scale_chi2_zeta']} (upper plots of each panel), as indicated in the top label. Here, we show the results at $z = 0$, with a different color for each neutrino mass, as indicated in the legend. The inset plots in the upper row show the multipoles $\zeta_\ell(s_{12}, s_{13})$ from which the 3PCF has been reconstructed. The lower plots show the corresponding detectabilities as a function of $s_{23}$ (Eq. \ref{['eq:def_detectability']}). A blue dashed line marks the zero detectability level. The orange shaded areas show the region $90 \, \hbox{$h^{-1}$ Mpc} \leq s_{23} \leq 110 \, \hbox{$h^{-1}$ Mpc}$, corresponding to the expected location of the BAO peak. Where the BAO scales do not cover the full $s_{23}$ range, we include a zoom-in on the detectability in that region, to better visualize the impact of neutrinos in those ranges.
• Figure 3: Detectability matrices of massive neutrinos. Each matrix element shows the scale $s_{\mathrm{cross}}$ (Eq. \ref{['eq:scale_crossing']}) below which, considering all triangles with scale larger than $s_{\mathrm{cross}}$, we get a significant detection of the signal from massive neutrinos in the connected 3PCF. The matrices in the upper and lower rows show the values for a $1\sigma$ and $3\sigma$ statistical significance (Eq. \ref{['eq:signif']}), respectively, computed for a volume of $10 \, \hbox{$h^{-3}$ Gpc$^3$}$. In each matrix, $M_\nu$ increases from left to right, and redshifts from bottom to top. We show the results for the three configurations corresponding to the lines in Fig. \ref{['fig:single_scale_chi2_zeta']}, i.e., from left to right: triangles with $s_{12} = 10 \, \hbox{$h^{-1}$ Mpc}$, isosceles triangles ($\eta = 0$), and quasi-isosceles triangles with $\eta = 4$. The quantity $s_{\mathrm{cross}}$ represents one of the two sides, $s_{12}$ or $s_{13}$, depending on the configuration: in particular, in Eq. \ref{['eq:scale_crossing']} we set $s = s_{13}$ for triangles with fixed $s_{12}$, and $s = s_{12}$ for isosceles and $\eta = 4$ triangles. Brighter colors represent better detection levels, i.e., occurring at larger scales. The label "ND" stands for "not detectable" above the specified significance threshold at any scale. A lower limit is indicated whenever the signal is detectable above a given threshold of statistical significance over the entire range of scales considered in our analysis.
• Figure 4: The detectability of the halo connected 3PCF (upper panels) and reduced 3PCF (lower panels) as a function of the triangle shape. Here, the results are reported at $z = 0$ and for $M_\nu = 0.4$ eV. The triangle shapes are determined by the side ratios $s_{12}/s_{23}$ and $s_{13}/s_{23}$, with $s_{12} \leq s_{13} \leq s_{23}$. In each panel, each pixel represents a given triangle shape, where the color shows the absolute value of the detectability averaged over all the triangles available in the all-scales approach with that shape and different sizes. As shown in the legend in the upper-right panel, the bottom center, upper-right, and upper-left parts of the plot contain, respectively, folded, equilateral, and squeezed triangles. The dotted curve in the lower-right panel marks the location of right-angled triangles. The white region corresponds to the area in the parameter space where it is not possible to obtain a closed triangle. The various columns differ by the range of $s_{23}$ considered, specified in the intervals shown in the bottom-right corner (in units of $h^{-1}$ Mpc). Empty bins are colored in grey.
• Figure 5: Comparison between the detectability of a variation in $M_\nu$ and $\sigma_8$ from the halo 3PCF as a function of triangle shape. We show the results for the simulations at $z = 0$ with $M_\nu = 0.1$ eV and fiducial $\sigma_8 = 0.834$ (red-scale colormaps), and with $M_\nu = 0$ eV and $\sigma_8 = 0.849$ (upper blue-scale colormap) and $\sigma_8 = 0.819$ (lower blue-scale colormap). The top and bottom pairs of plots refer to the connected and reduced 3PCF, respectively. Triangle shapes are identified by the side ratios $s_{12}/s_{23}$ and $s_{13}/s_{23}$, with $s_{12} \leq s_{13} \leq s_{23}$, as shown in Fig. \ref{['fig:shape_plots']}. In each plot, a given shape bin shows the absolute value of the detectability, averaged over all triangles available in the all-scales approach with that shape and different sizes. In this figure, we present the results obtained by considering triangles on scales $30 \, \hbox{$h^{-1}$ Mpc} < s_{23} < 70 \, \hbox{$h^{-1}$ Mpc}$ for $\zeta$, and $70 \, \hbox{$h^{-1}$ Mpc} < s_{23} < 110 \, \hbox{$h^{-1}$ Mpc}$ for $Q$.