Speaker
Description
The matter field in the universe is a Gaussian Random Field on large scales and early times, summarized by the power spectrum or two-point correlation function. However, on smaller scales and late times, non-linear gravitational evolution results in non-Gaussian clustering, necessitating improved summary statistics. k-Nearest Neighbour Cumulative Distribution Functions ($k$NN CDFs) are sensitive to all connected N-point correlation functions, while being much faster to compute.
In my talk, I will show some recent developments regarding the kNN statistics. I will demonstrate the geometric interpretation of these statistics, and their relation with other geometric and topological statistics. ${\rm CDF}_{1{\rm NN}}(r)$ reflects the volume fraction within spheres of radius r centered on tracers. Its derivatives relate to the geometry of sphere intersections, equivalent to the information provided by Minkowski functionals (volume, area, mean curvature, and Euler characteristic), but being computationally more efficient.
We extend the $k$NN CDF formalism to cross-correlations between tracers and fields. The 21cm radiation field during the Epoch of Reionization has a bubble morphology driven by ionising radiation from galaxies, making it a natural target for kNN analysis, which is particularly sensitive to spherical structure around tracers. We apply this formalism to measure the cross-correlation between galaxies and the HI field during reionization, and find that kNN cross-correlations outperform the standard 2-point cross-correlation even in the presence of foreground and instrumental noise. The kNN statistics are even able to distinguish between reionization models that are indistinguishable with the 2-point function alone.
With upcoming surveys and telescopes such as DESI, Euclid, and SKA set to probe these non-linear scales, the $k$NN framework offers a fast, effective, and versatile tool for next-generation cosmological analyses.
| Other topic / keywords: | Reionization, 21cm cosmology |
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