Small-scale signatures of primordial non-Gaussianity in k-Nearest Neighbour cumulative distribution functions

Searches for primordial non-Gaussianity in cosmological perturbations are a key means of revealing novel primordial physics. However, robustly extracting signatures of primordial non-Gaussianity from non-linear scales of the late-time Universe is an open problem. In this paper, we apply k-Nearest Neighbor cumulative distribution functions, kNN-CDFs, to the \textsc{quijote-png} simulations to explore the sensitivity of kNN-CDFs to primordial non-Gaussianity. An interesting result is that for halo samples with $M_h<10^{14}$ M$_\odot$/h, the kNN-CDFs respond to \textit{equilateral} PNG in a manner distinct from the other parameters. This persists in the galaxy catalogs in redshift space and can be differentiated from the impact of galaxy modelling, at least within the halo occupation distribution (HOD) framework considered here. kNN-CDFs are related to counts-in-cells and, through mapping a subset of the kNN-CDF measurements into the count-in-cells picture, we show that our results can be modeled analytically. A caveat of the analysis is that we only consider the HOD framework, including assembly bias. It will be interesting to validate these results with other techniques for modeling the galaxy--halo connection, e.g., (hybrid) effective field theory or semi-analytical methods.