High order correction terms for the peak-peak correlation function in nearly-Gaussian models

Abstract

Context. One possible way to investigate the nature of the primordial power spectrum fluctuations is by investigating the statistical properties of the local maximum in the density fluctuation fields.Aims. In this work we present a study of the mean correlation function, ξ r , and the correlation function for high-amplitude fluctuations (peak-peak correlation) in a slighlty non-Gaussian context. Methods. From the definition of the correlation excess, we computed the Gaussian two-point correlation function and, using an expansion in generalized Hermite polynomials, we estimated the correlation of high-density peaks in a non-Gaussian field with a generic distribution and power spectrum. We also applied the results to a scale-mixed distribution model, which corresponds to a nearly Gaussian model. Results. The results reveal that, even for a small deviation from Gaussianity, we can expect high-density peaks to be much more correlated than in a Gaussian field with the same power spectrum. In addition, the calculations reveal how the amplitude of the peaks in the fluctuation field is related to the existing correlations. Conclusions. Our results may be used as an additional tool for investigating the behavior of the N-point correlation function, to understand how non-Gaussian correlations affect the peak-peak statistics, and extract more information about the statistics of the density field.

Primordial non-Gaussianity from the large-scale structure

“…Before this was realized, it was argued that primeval fluctuations need to be non-Gaussian [139,140] to explain the observed strong correlation of Abell clusters [141,142]. Along these lines, [143] pointed out that primordial non-Gaussianity could significantly increase the amplitude of the two-point correlation of galaxies and clusters on large scales, However, except from [144] who showed that correlations of high density peaks in non-Gaussian models are significantly stronger than in the Gaussian model with identical mass power spectrum, subsequent work focused mostly on abundances ( §4.2) or higher order statistics such as the bispectrum ( §4.4). It is only recently that [13] have demonstrated the strong scaledependent bias arising in non-Gaussian models of the local f loc NL type.…”

Primordial Non‐Gaussianity in the Large‐Scale Structure of the Universe

“…Along these lines, [155] pointed out that primordial non-Gaussianity could significantly increase the amplitude of the two-point correlation of galaxies and clusters on large scales. However, except from [156] who showed that correlations of high density peaks in non-Gaussian models are significantly stronger than in the Gaussian model with identical mass power spectrum, subsequent work focused mostly on abundances ( §IV B) or higher order statistics such as the bispectrum ( §IV D). It is only recently that [12] have demonstrated the strong scale-dependent bias arising in non-Gaussian models of the local f loc NL type.…”

Statistics of peaks of weakly non-Gaussian random fields: Effects of bispectrum in two- and three-dimensions

“…The peak correlations in weakly non-Gaussian fields are derived [59], which are applied to a local-type non-Gaussianity in the primordial density field. Abundances and correlations of peaks in weakly non-Gaussian field in the high-peak limit are also derived [60][61][62][63].…”