Modelling kNN-CDFs of biased tracers in redshift space using hybrid Lagrangian bias expansion

Abstract

Higher-order statistics are becoming increasingly useful in clustering studies of the large-scale structure (LSS) of the universe. The kNN-CDFs are one such higher-order statistic, sensitive to all N-point correlations and easy to compute on data. Utilising their statistical gains for cosmological inference requires modelling them accurately for the tracer of interest. We use the hybrid Lagrangian bias expansion to enable this modelling in redshift space, building and validating the pipeline on Quijote simulations. We show that the kNN-CDFs of a luminous red galaxy (LRG)-like sample can be modelled down to scales as small as r = 10 Mpc/h, with the minimum reliable scale increasing with nearest-neighbour order. Moreover, the model parameters inferred from the kNN-CDFs also describe the galaxy power spectrum P(k), indicating model consistency across the two statistics and the feasibility of combining them. Fisher forecasts for galaxy auto clustering show that combining P(k) and kNN-CDFs improves constraints on all parameters relative to either statistic alone. Relative to P(k), the constraints on $b_3$ improve the most, while those on $σ_8$ and $Ω_m$ improve by factors of 3.5 and 1.7, respectively. Including galaxy-matter cross clustering alongside galaxy auto clustering further improves the Fisher constraints from both P(k) and kNN-CDFs, with their combination yielding the tightest constraints overall. Relative to P(k), the largest improvement from this combination is found for $b_2$, while the constraints on $σ_8$ and $Ω_m$ improve by factors of 4.2 and 1.7, respectively. These results demonstrate the applicability of the hybrid Lagrangian bias framework to model the kNN-CDFs of biased tracers in redshift space, and the potential of combining higher-order and two-point statistics to extract cosmological information.