Cosmological cross-correlations and nearest neighbour distributions

Banerjee, Arka; Abel, Tom

doi:10.1093/mnras/stab961

Cited by 37 publications

(20 citation statements)

References 67 publications

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“…The value of CDF 𝑘 1 ,𝑘 2 at volume 𝑉 corresponds to the probability of finding more than 𝑘 1 data points from set 1 and 𝑘 2 data points from set 2 in volume 𝑉. As shown in Banerjee & Abel (2021b), this joint CDF 𝑘 1 ,𝑘 2 captures the auto-clustering of the two datasets, along with the cross-correlations between them.…”

Section: Formalism and Calculation Frameworkmentioning

confidence: 97%

“…5, it is clear that each 𝑘NN-CDF measurement is sensitive to a different combination of the integrals of various 𝑁-point functions of the underlying field. Banerjee & Abel (2021b) demonstrated the extension of the 𝑘NN framework to the joint CDFs of two sets of tracers -𝑁 1 tracers of type 1 and 𝑁 2 tracers of type 2 distributed over a total volume 𝑉 tot . The joint CDF 𝑘 1 ,𝑘 2 is computed by measuring the distances to the 𝑘 1 -th nearest neighbor data point from set 1 and 𝑘 2 -th nearest neighbor from set 2 from a set of query points, and then considering the CDF of the larger of these two distances for every query point.…”

Section: Formalism and Calculation Frameworkmentioning

confidence: 99%

“…For the 𝑘NN-CDF measurements, we simply choose two disjoint subsets of 10 5 simulation particles from the set of all simulation particles. We then compute CDF 1,1 using the process outlined in Banerjee & Abel (2021b). To make predictions for CDF 1,1 from the underlying matter field, we use the fact that this situation corresponds to setting 𝜆 1,𝑖 = 𝜆 2,𝑖 = 𝜆 𝑖 in Eq.…”

Section: 𝑘Nn-cdfs Of the Matter Density Fieldmentioning

confidence: 99%

“…Further, the bottom right panel shows that the same general agreement is also seen for the joint CDF 1,1 between the halos and particles. This particular measurement is sensitive not only to all higher order 𝑁-point functions of the halo sample, but also to higher order 𝑁-point functions of the matter field, as well as all possible 𝑁-point functions that can be defined in terms of various combinations of the two fields (Banerjee & Abel 2021b). Therefore, the HEFT formalism can potentially fit not just the two-point clustering of the halo sample in terms of the two point functions of various advected Lagrangian fields, but also various higher order statistics.…”

Section: Using Best-fit Bias Values From 2-point Clusteringmentioning

confidence: 99%

“…If the tracers represent a local Poisson sampling of an underlying field, the 𝑘NN-CDFs are sensitive to integrals of all connected 𝑁point functions of the underlying field. For two sets of tracers, and their corresponding underlying fields, Banerjee & Abel (2021b) demonstrated that the joint 𝑘NN-CDFs are sensitive to all combinations of 𝑁-point functions that can be formed from the two fields. This makes these statistics a powerful probe of clustering, and was recently applied to the measurement of the clustering of very massive galaxy clusters (Wang et al 2021).…”

Section: Introductionmentioning

confidence: 99%

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Modelling nearest neighbour distributions of biased tracers using hybrid effective field theory

Banerjee

Kokron

Abel

2022

Monthly Notices of the Royal Astronomical Society

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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 (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−1Mpc) 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 σ8 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.

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Section: Formalism and Calculation Frameworkmentioning

confidence: 97%

Section: Formalism and Calculation Frameworkmentioning

confidence: 99%

Section: 𝑘Nn-cdfs Of the Matter Density Fieldmentioning

confidence: 99%

Section: Using Best-fit Bias Values From 2-point Clusteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling nearest neighbour distributions of biased tracers using hybrid effective field theory

Banerjee

Kokron

Abel

2022

Monthly Notices of the Royal Astronomical Society

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Large-scale dark matter simulations

Angulo

Hahn

2022

Living Rev Comput Astrophys

111

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We review the field of collisionless numerical simulations for the large-scale structure of the Universe. We start by providing the main set of equations solved by these simulations and their connection with General Relativity. We then recap the relevant numerical approaches: discretization of the phase-space distribution (focusing on N-body but including alternatives, e.g., Lagrangian submanifold and Schrödinger–Poisson) and the respective techniques for their time evolution and force calculation (direct summation, mesh techniques, and hierarchical tree methods). We pay attention to the creation of initial conditions and the connection with Lagrangian Perturbation Theory. We then discuss the possible alternatives in terms of the micro-physical properties of dark matter (e.g., neutralinos, warm dark matter, QCD axions, Bose–Einstein condensates, and primordial black holes), and extensions to account for multiple fluids (baryons and neutrinos), primordial non-Gaussianity and modified gravity. We continue by discussing challenges involved in achieving highly accurate predictions. A key aspect of cosmological simulations is the connection to cosmological observables, we discuss various techniques in this regard: structure finding, galaxy formation and baryonic modelling, the creation of emulators and light-cones, and the role of machine learning. We finalise with a recount of state-of-the-art large-scale simulations and conclude with an outlook for the next decade.

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Bounds on galaxy stochasticity from halo occupation distribution modeling

Britt,

Gruen,

Friedrich

et al. 2024

A&A

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The joint probability distribution of matter overdensity and galaxy counts in cells is a powerful probe of cosmology, and the extent to which variance in galaxy counts at fixed matter density deviates from Poisson shot noise is not fully understood. The lack of informed bounds on this stochasticity is currently the limiting factor in constraining cosmology with the galaxy--matter probability distribution function (PDF). We investigate stochasticity in the conditional distribution of galaxy counts along lines of sight with fixed matter density, and we present a halo occupation distribution (HOD)-based approach for obtaining plausible ranges for stochasticity parameters. To probe the high-dimensional space of possible galaxy--matter connections, we derive a set of HODs that conserve the galaxies' linear bias and number density to produce redMaGiC -like galaxy catalogs within the AbacusSummit suite of $N$-body simulations. We study the impact of individual HOD parameters and cosmology on stochasticity and perform a Monte Carlo search in HOD parameter space subject to the constraints on bias and density. In mock catalogs generated by the selected HODs, shot noise in galaxy counts spans both sub-Poisson and super-Poisson values, ranging from 80<!PCT!> to 133<!PCT!> of Poisson variance for cells with mean matter density. Nearly all of the derived HODs show a positive relationship between local matter density and stochasticity. For galaxy catalogs with higher stochasticity, modeling galaxy bias to second order is required for an accurate description of the conditional PDF of galaxy counts at fixed matter density. The presence of galaxy assembly bias also substantially extends the range of stochasticity in the super-Poisson direction. This HOD-based approach leverages degrees of freedom in the galaxy--halo connection to obtain informed bounds on nuisance model parameters and can be adapted to study other parametrizations of shot noise in galaxy counts, in particular to motivate prior ranges on stochasticity for cosmological analyses.

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Cosmological cross-correlations and nearest neighbour distributions

Cited by 37 publications

References 67 publications

Modelling nearest neighbour distributions of biased tracers using hybrid effective field theory

Modelling nearest neighbour distributions of biased tracers using hybrid effective field theory

Large-scale dark matter simulations

Bounds on galaxy stochasticity from halo occupation distribution modeling

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