Primordial non-Gaussianity from the covariance of galaxy cluster counts

Carlos Cunha, Dragan Huterer, and Olivier Doré

Phys. Rev. D 82, 023004 – Published 19 July 2010

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 3 (1) 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 Dark Energy Survey can yield constraints on non-Gaussianity of $σ (f_{NL}) \sim 1 - 5$ 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.

Received 17 March 2010

DOI:https://doi.org/10.1103/PhysRevD.82.023004

Authors & Affiliations

Carlos Cunha¹, Dragan Huterer¹, and Olivier Doré^2,3

¹Department of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040, USA
²Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA
³California Institute of Technology, Pasadena, California 91125, USA

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Vol. 82, Iss. 2 — 15 July 2010

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Images

Figure 1
Left panel: Sensitivity of the variance of cluster counts to non-Gaussianity. The black lines shows the variance $S_{i i}$ , the short dashed red line shows the (auto)correlation function $ξ_{i i}^{α}$ , and the long-dashed blue line shows the squared mean counts. Note that $S_{i i} = (\bar{m})^{2} ξ_{i i}^{α}$ . We assumed a pixel with area 40 sq. deg and radial redshift extent $Δ z = 0.2$ , 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 $f_{NL} = 0$ case ( $S_{i i}^{Gauss}$ ) 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 ( $f_{NL} = 0$ ), and four non-Gaussian models ( $f_{NL} = \pm 20$ and $f_{NL} = \pm 100$ ). 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.Reuse & Permissions
Figure 2
$1 − σ$ uncertainties in the parameter $f_{NL}$ 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 Oguri [52]). The maximum angular separation between pixels for a 5000 sq. deg survey divided into 41.3 sq. deg pixels is about 90 deg (or $10 \sqrt{2}$ pixel widths). This case would correspond to taking the full covariance into account for the calculation of $f_{NL}$ , 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.Reuse & Permissions
Figure 3
Left panel: Unmarginalized $1 − σ$ constraints on $f_{NL}$ 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 $f_{NL}$ , and the total covariance at the fiducial $f_{NL}$ ; see text. Right panel: Derivative of the signal matrix elements $S_{i j}$ with respect to $f_{NL}$ as a function of angular separation between pixels $i$ and $j$ , for $f_{NL} = - 40$ , $- 20$ , 0, 20, and 40. Recall that, at $z = 0.5$ , a separation of 1 deg corresponds to about $23 h^{- 1} Mpc$ .Reuse & Permissions

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