Primordial non-Gaussianity from the covariance of galaxy cluster counts

TL;DR

This study shows that primordial non-Gaussianity of the local type, quantified by $f_{NL}$, leaves a distinctive imprint on the covariance of galaxy cluster counts across large scales via the scale-dependent halo bias. By formulating a pixelized counts-in-cells approach that incorporates both cluster counts and their full covariance, and by regularizing the large-scale limit, the authors forecast DES-like constraints that can reach $\sigma(f_{NL})$ on the order of 1–5 under conservative systematics. The key insight is that far-apart cluster covariances carry the strongest $f_{NL}$ signal due to the $k^{-2}$ bias term, and that including this information dramatically improves constraints compared to counts alone or counts+variance, while remaining robust to degeneracies with other parameters when Planck priors are used. Photometric redshift uncertainties and mass-observable systematics are shown to be manageable with informative priors, making the proposed covariance-based method a powerful probe of primordial non-Gaussianity with upcoming large-scale structure surveys.

Abstract

It has recently been proposed that the large-scale bias of dark matter halos depends sensitively on primordial non-Gaussianity of the local form. In this paper we point out that the strong scale dependence of the non-Gaussian halo bias imprints a distinct signature on the covariance of cluster counts. We find that using the full covariance of cluster counts results in improvements on constraints on the non-Gaussian parameter f_NL of three (one) orders of magnitude relative to cluster counts (counts + clustering variance) constraints alone. We forecast f_NL constraints for the upcoming Dark Energy Survey in the presence of uncertainties in the mass-observable relation, halo bias, and photometric redshifts. We find that the DES can yield constraints on non-Gaussianity of sigma(f_NL) ~ 1-5 even for relatively conservative assumptions regarding systematics. Excess of correlations of cluster counts on scales of hundreds of megaparsecs would represent a smoking gun signature of primordial non-Gaussianity of the local type.

Figures (3)

• Figure 1: Left panel: Sensitivity of the variance of cluster counts to non-Gaussianity. The black lines shows the variance $S_{ii}$, the short-dashed red line shows the (auto)correlation function $\xi_{ii}^{\alpha}$, and the long-dashed blue line shows the squared mean counts. Note that $S_{ii}=({\bar{m}})^2\xi_{ii}^{\alpha}$ We assumed a pixel with area 40 sq. deg. and radial redshift extent $\Delta z=0.2$, centered at $z=0.5$. Right panel: Sensitivity of the covariance of cluster counts to non-Gaussianity. We show the off-diagonal elements of the clustering matrix, normalized by the variance of $f_{\rm NL}=0$ case ($S_{ii}^{\rm Gauss}$) as a function of angle between the $i$th and $j$th pixel. We use the same pixelization as for the left panel. We show the Gaussian case ($f_{\rm NL}=0$), and four non-Gaussian models ($f_{\rm NL}=\pm 20$ and $f_{\rm NL}=\pm 100$). Note that, because of the regularization, the results depend on the size of the survey. The larger the survey, the larger the effect of non-Gaussianity.
• Figure 2: $1-\sigma$ uncertainties in the parameter $f_{\rm NL}$ as a function of the maximum angular separation between pixel centroids in the covariance matrix. The left panel shows the unmarginalized constraints while the right panel shows marginalized constraints assuming Planck priors and fixed halo-bias and observable-mass nuisance parameters. Zero separation indicates the case of pure variances (as considered by Oguri09). The maximum angular separation between pixels for a $5,000$ sq. deg. survey divided into 41.3 sq. deg pixels is about 90 degrees (or $10\sqrt{2}$ pixel widths). This case would correspond to taking the full covariance into account for the calculation of $f_{\rm NL}$, but disregarding the covariance between different redshift bins. The blue short dashed line corresponds to constraints derived using only cluster counts. The red dashed line shows the constraints when only the clustering of clusters is used, and the solid black line shows the combined constraints from counts and clustering.
• Figure 3: Left panel: Unmarginalized $1-\sigma$ constraints on $f_{\rm NL}$ as a function of the fiducial value of this parameter, assuming five redshift and five mass bins. The "witch's hat" shape can be explained from the competition between the derivative of the covariance with respect to $f_{\rm NL}$, and the total covariance at the fiducial $f_{\rm NL}$; see text. Right panel: Derivative of the signal matrix elements $S_{ij}$ with respect to $f_{\rm NL}$ as a function of angular separation between pixels $i$ and $j$, for $f_{\rm NL}=-40, -20, 0, 20$, and $40$. Recall that, at $z=0.5$, a separation of 1 degree corresponds to about $23h^{-1}$Mpc.