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 simulationsto the modeling of 𝑘-Nearest Neighbor Cumulative Distribution Functions (𝑘NN-CDFs) of biased tracers of the cosmological matter field. The 𝑘NN-CDFs 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 𝑘NN-CDFs of discrete tracers of a continuous field from the statistics of the continuous field itself. Using this formalism, we demonstrate how 𝑘NN-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 and the 𝑘NN-CDFs can be well-fit on quasi-linear scales ( 20ℎ −1 Mpc) by the second-order HEFT formalism with the 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 𝑘NN-CDF measurements over the range of allowed scales in the HEFT framework can improve the constraints on 𝜎 8 by roughly a factor of 3, compared to the case where only two-point measurements are considered. Combining the statistical power of 𝑘NN measurements with the modeling power of HEFT, therefore, represents an exciting prospect for extracting greater information from small-scale cosmological clustering.

Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology

“…Additionally, we note that the DTM function also gives us precise information regarding the distances to nearest neighbors of a point. Recently, the distribution of such distances has been considered as a summary statistic in its own right [9][10][11]. Results from those works suggest that it could be beneficial to simultaneously consider the topology for different values of k.…”

“…1 More broadly, a central problem in modern cosmology is the extraction of maximum information content regarding the universe's initial conditions and dynamics from observations. Beyond the traditional program of low-order correlation functions in Fourier space, there is an ongoing effort to characterize cosmological information content of real-space and higher-order statistics such as the k-nearest neighbor distribution [9][10][11] and one-point PDF [12][13][14][15][16]. Several of the present authors recently proposed a new class of statistics derived from computational topology for this purpose [17].…”

Large-scale dark matter simulations

“…Another potentially more robust option has been proposed recently in terms of combinations of parametric bias descriptions (motivated by perturbative expansion of galaxy bias) with N -body dynamics, which can be emulated efficiently and could be a robust way to extract information from the quasi-linear regime. In the future the main challenges will be the extension to include peculiar velocities and a self-consistent treatment of higher-order correlations (Pellejero-Ibanez et al 2021;Banerjee et al 2021). It is commonly argued that by using measurements of the late-time LSS, one can access a large number of modes in the Universe which can potentially outperform CMB analysis.…”

Detection of spatial clustering in the 1000 richest SDSS DR8 redMaPPer clusters with nearest neighbor distributions

“…Given its extra sensitivity to all higher-order correlation functions, while maintaining feasible computational demand, the kNN summary statistics provides a much more powerful yet resource-efficient probe of cosmology than the two-point correlation function. On quasi-linear scales, kNN distributions of tracers can be modeled using the same set of parameters (Banerjee et al 2021) that are used to model the twopoint correlation function in this regime (e.g. Kokron et al 2021).…”