Modeling Nearest Neighbor distributions of biased tracers using Hybrid Effective Field Theory

Abstract

We investigate the application of Hybrid Effective Field Theory (HEFT) -- which combines a Lagrangian bias expansion with subsequent particle dynamics from $N$-body simulations -- to the modeling of $k$-Nearest Neighbor Cumulative Distribution Functions ($k\mathrm{NN}$-$\mathrm{CDF}$s) of biased tracers of the cosmological matter field. The $k\mathrm{NN}$-$\mathrm{CDF}$s are sensitive to all higher order connected $N$-point functions in the data, but are computationally cheap to compute. We develop the formalism to predict the $k\mathrm{NN}$-$\mathrm{CDF}$s of discrete tracers of a continuous field from the statistics of the continuous field itself. Using this formalism, we demonstrate how $k\mathrm{NN}$-$\mathrm{CDF}$ statistics of a set of biased tracers, such as halos or galaxies, of the cosmological matter field can be modeled given a set of low-redshift HEFT component fields and bias parameter values. These are the same ingredients needed to predict the two-point clustering. For a specific sample of halos, we show that both the two-point clustering \textit{and} the $k\mathrm{NN}$-$\mathrm{CDF}$s can be well-fit on quasi-linear scales ($\gtrsim 20h^{-1}\mathrm{Mpc}$) by the second-order HEFT formalism with the \textit{same values} of the bias parameters, implying that joint modeling of the two is possible. Finally, using a Fisher matrix analysis, we show that including $k\mathrm{NN}$-$\mathrm{CDF}$ measurements over the range of allowed scales in the HEFT framework can improve the constraints on ${\sigma }_8$ by roughly a factor of $3$, compared to the case where only two-point measurements are considered. Combining the statistical power of $k\mathrm{NN}$ measurements with the modeling power of HEFT, therefore, represents an exciting prospect for extracting greater information from small-scale cosmological clustering.

Accepted to MNRAS. Matches accepted version

References in corpus (10)

• The DESI Experiment Part I: Science,Targeting, and Survey Design
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• The Cosmic Code Comparison Project
• Constraining $M_{\nu }$ with the Bispectrum II: The Total Information Content of the Galaxy Bispectrum
• The Gaussian streaming model and Lagrangian effective field theory
• Simulations and symmetries
• Hefty enhancement of cosmological constraints from the DES Y1 data using a Hybrid Effective Field Theory approach to galaxy bias
• Shot noise and biased tracers: a new look at the halo model
• The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

Cited by in corpus (18)

• Large-scale dark matter simulations
• The MillenniumTNG Project: An improved two-halo model for the galaxy-halo connection of red and blue galaxies
• Aemulus $\nu$: Precise Predictions for Matter and Biased Tracer Power Spectra in the Presence of Neutrinos
• Priors on red galaxy stochasticity from hybrid effective field theory
• Accurate predictions from small boxes: variance suppression via the Zel'dovich approximation
• Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology
• Tracer-Field Cross-Correlations with $k$-Nearest Neighbor Distributions
• HYMALAIA: A Hybrid Lagrangian Model for Intrinsic Alignments
• Non-parametric reconstruction of cosmological observables using Gaussian Processes Regression
• Cosmological Probes of Structure Growth and Tests of Gravity
• Cosmology with Persistent Homology: a Fisher Forecast
• Detection of spatial clustering in the 1000 richest SDSS DR8 redMaPPer clusters with Nearest Neighbor distributions
• 2D k-th nearest neighbor statistics: a highly informative probe of galaxy clustering
• Geometric Interpretations of the $k$-Nearest Neighbour Distributions
• One-point Statistics in various cosmic environments in the presence of massive neutrinos
• Clustering of dark matter in the cosmic web as a probe of massive neutrinos
• Nearest Neighbour-Based Statistics for 21cm-Galaxy Cross-Correlations in the Epoch of Reionization
• Sahyadri: A simulation suite for the cosmology dependence of the Cosmic Web