1.9k citations · 4k across the 80 of their papers we have counts for
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On a General Method for Resolving Integrals of Multiple Spherical Bessel Functions Against Power Laws into Distributions
Kiersten Meigs, Zachary Slepian
We here present a method of performing integrals of products of spherical Bessel functions (SBFs) weighted by a power-law. Our method, which begins with double-SBF integrals, explo…
Accelerating BAO Scale Fitting Using Taylor Series
Matthew Hansen, Alex Krolewski, Zachary Slepian
The Universe is currently undergoing accelerated expansion driven by dark energy. Dark energy's essential nature remains mysterious: one means of revealing it is by measuring the U…
A Test for Cosmological Parity Violation Using the 3D Distribution of Galaxies
Robert N. Cahn, Zachary Slepian, Jiamin Hou
We show that the galaxy 4-Point Correlation Function (4PCF) can test for cosmological parity violation. The detection of cosmological parity violation would reflect previously unkn…
Analytic Gaussian Covariance Matrices for Galaxy -Point Correlation Functions
Jiamin Hou, Robert N. Cahn, Oliver H. E. Philcox +1
We derive analytic covariance matrices for the -Point Correlation Functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary and projected onto…
A First Detection of the Connected 4-Point Correlation Function of Galaxies Using the BOSS CMASS Sample
Oliver H. E. Philcox, Jiamin Hou, Zachary Slepian
We present an detection of the non-Gaussian 4-Point Correlation Function (4PCF) using a sample of galaxies from the BOSS CMASS dataset. Our…
Clustering in Massive Neutrino Cosmologies via Eulerian Perturbation Theory
Alejandro Aviles, Arka Banerjee, Gustavo Niz +1
We introduce an Eulerian Perturbation Theory to study the clustering of tracers for cosmologies in the presence of massive neutrinos. Our approach is based on mapping recently-obta…
Efficient Computation of -point Correlation Functions in Dimensions
Oliver H. E. Philcox, Zachary Slepian
We present efficient algorithms for computing the -point correlation functions (NPCFs) of random fields in arbitrary -dimensional homogeneous and isotropic spaces. Such stati…
An Exact Integral-to-Sum Relation for Products of Bessel Functions
Oliver H. E. Philcox, Zachary Slepian
A useful identity relating the infinite sum of two Bessel functions to their infinite integral was discovered in Dominici et al. (2012). Here, we extend this result to products of…
ENCORE: An Estimator for Galaxy -Point Correlation Functions
Oliver H. E. Philcox, Zachary Slepian, Jiamin Hou +3
We present a new algorithm for efficiently computing the -point correlation functions (NPCFs) of a 3D density field for arbitrary . This can be applied both to a discrete spe…
A Uniform Spherical Goat (Problem): Explicit Solution for Homologous Collapse's Radial Evolution in Time
Zachary Slepian, Oliver H. E. Philcox
The homologous collapse from rest of a uniform density sphere under its self gravity is a well-known toy model for the formation dynamics of astronomical objects ranging from stars…
Kepler's Goat Herd: An Exact Solution to Kepler's Equation for Elliptical Orbits
Oliver H. E. Philcox, Jeremy Goodman, Zachary Slepian
A fundamental relation in celestial mechanics is Kepler's equation, linking an orbit's mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation ca…
Information Content of Higher-Order Galaxy Correlation Functions
Lado Samushia, Zachary Slepian, Francisco Villaescusa-Navarro
The shapes of galaxy N-point correlation functions can be used as standard rulers to constrain the distance-redshift relationship and thence the expansion rate of the Universe. The…
Beyond Yamamoto: Anisotropic Power Spectra and Correlation Functions with Pairwise Lines-of-Sight
Oliver H. E. Philcox, Zachary Slepian
Conventional estimators of the anisotropic power spectrum and two-point correlation function (2PCF) adopt the `Yamamoto approximation', fixing the line-of-sight of a pair of galaxi…