Statistics of the excursion sets in models with local primordial non-Gaussianity

TL;DR

This paper investigates how local primordial non-Gaussianity affects the statistics and clustering of temperature excursion sets in the CMB, proposing tests to detect non-Gaussian signals and reduce cosmic variance.

Contribution

It introduces a comprehensive analysis of excursion set statistics in non-Gaussian models, including new methods to detect non-Gaussianity and optimize threshold selection.

Findings

Positive f_NL increases cold excursion set density and clustering.

Clustering signatures are most prominent at 75 arcmin scales.

Methods to minimize cosmic variance effects are proposed.

Abstract

We use the statistics of regions above or below a temperature threshold (excursion sets) to study the cosmic microwave background (CMB) anisotropy in models with primordial non-Gaussianity of the local type. By computing the full-sky spatial distribution and clustering of pixels above/below threshold from a large set of simulated maps with different levels of non-Gaussianity, we find that a positive value of the dimensionless non-linearity parameter f_NL enhances the number density of the cold CMB excursion sets along with their clustering strength, and reduces that of the hot ones. We quantify the robustness of this effect, which may be important to discriminate between the simpler Gaussian hypothesis and non-Gaussian scenarios, arising either from non-standard inflation or alternative early-universe models. The clustering of hot and cold pixels exhibits distinct non-Gaussian signatures, particularly at angular scales of about 75 arcmin (i.e. around the Doppler peak), which increase linearly with f_NL. Moreover, the clustering changes strongly as a function of the smoothing angle. We propose several statistical tests to maximize the detection of a local primordial non-Gaussian signal, and provide some theoretical insights within this framework, including an optimal selection of the threshold level. We also describe a procedure which aims at minimizing the cosmic variance effect, the main limit within this statistical framework.