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Theoretical and Observational Cosmology
Theoretical and Observational Cosmology
Higher-Order Statistics: Parity Violation, Neutrino Mass; Algorithms, Mathematical Methods, Star Formation: Theory and Data
Parity Violation
Parity Violation
We have shown that the galaxy 4-Point Correlation Function (4PCF) can probe parity violation in 3D large-scale structure, which, if there, would likely stem from the epoch of inflation. We developed a basis to measure the 4PCF, then proposed searching for parity violation with it, and finally performed the measurement. We appear to see a 7 sigma signal in one BOSS sample (CMASS, ~800,000 galaxies) and 3 sigma in another, smaller one (LOWZ, ~300,000 galaxies).
We have shown that the galaxy 4-Point Correlation Function (4PCF) can probe parity violation in 3D large-scale structure, which, if there, would likely stem from the epoch of inflation. We developed a basis to measure the 4PCF, then proposed searching for parity violation with it, and finally performed the measurement. We appear to see a 7 sigma signal in one BOSS sample (CMASS, ~800,000 galaxies) and 3 sigma in another, smaller one (LOWZ, ~300,000 galaxies).
Mathematical Basis
Cahn & Slepian, Isotropic N-point basis functions and their properties, Journal of Physics A: Mathematical and Theoretical. On arXiv here.
Slepian, Chellino, Hou, & Greco, On a generating function for the isotropic basis functions and other connected results, Journal of Physics A: Mathematical and Theoretical. On arXiv here.
Proposal for Parity Search with 4PCF
Cahn, Slepian, & Hou, Test for Cosmological Parity Violation Using the 3D Distribution of Galaxies, PRL. On arXiv here.
Analytic Covariance Matrix Template
Hou, Cahn, Philcox, & Slepian, Analytic Gaussian covariance matrices for galaxy N-point correlation functions, PRD. On arXiv here.
Search on SDSS BOSS CMASS and LOWZ data
Hou, Slepian, & Cahn, Measurement of parity-odd modes in the large-scale 4-point correlation function of Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey twelfth data release CMASS and LOWZ galaxies, MNRAS. On arXiv here.
Follow-up papers by our group and collaborators
One possible model for these results
Reinhard, Slepian, Hou & Greco, Full Parity-Violating Trispectrum in Axion Inflation: Reduction to Low-D Integrals, in submission.
Model for the even-parity, gravitationally-induced 4PCF, useful to calibrate the odd 4PCF covariance
Ortola-Leonard, Slepian & Hou, A Model for the Redshift-Space Galaxy 4-Point Correlation Function. Accepted JCAP, on arXiv here.
Use of BAO to verify the odd 4PCF, and as a standard ruler within it
Hou, Slepian & Jamieson, Can Baryon Acoustic Oscillations Illuminate the Parity-Violating Galaxy 4PCF?, in submission.
A new, compressed statistic to look for parity violation
Jamieson, Caravano, Hou, Slepian & Komatsu, Parity-Odd Power Spectra: Concise Statistics for Cosmological Parity Violation, MNRAS. On arXiv here.
Method to produce a density field with any desired NPCFs (useful for testing parity search systematics)
Slepian, Algorithm to produce a density field with given two-, three-, and four-point correlation functions, RAS Techniques and Instruments. On arXiv here.
Neutrino Mass
Neutrino Mass
We have developed a new signature of the neutrino mass, specifically, in how it alters the way different Fourier modes of the large-scale structure couple to each other as gravity induces nonlinear structure formation. This leads to new terms in the bispectrum (Fourier space analog of the 3-Point Correlation Function) that can be sought with BOSS and DESI.
We have developed a new signature of the neutrino mass, specifically, in how it alters the way different Fourier modes of the large-scale structure couple to each other as gravity induces nonlinear structure formation. This leads to new terms in the bispectrum (Fourier space analog of the 3-Point Correlation Function) that can be sought with BOSS and DESI.
Kamalinejad & Slepian, A Non-Degenerate Neutrino Mass Signature in the Galaxy Bispectrum, in submission.
We also performed the first fully analytic derivation of the shape of the neutrino-mass-induced decrement in the matter power spectrum.
Kamalinejad & Slepian, A Two-Fluid Treatment of the Effect of Neutrinos on the Matter Density, in submission.
Algorithms
Algorithms
The group has pushed forwards a number of algorithms, both those solving problems that were previously not solved, and those accelerating problems with standard, slower implementations.
The group has pushed forwards a number of algorithms, both those solving problems that were previously not solved, and those accelerating problems with standard, slower implementations.
Measurement of N-Point Correlation Functions
Slepian, Warner, Hou, Cahn & Eisenstein, CADENZA: A GPU-Accelerated Spherical Harmonic Code for NPCFs, in prep. (coming soon!)
Philcox, Slepian, Hou, Warner, Cahn, & Eisenstein, ENCORE: an O (Ng2) estimator for galaxy N-point correlation functions, MNRAS.
Philcox & Slepian, Efficient computation of N-point correlation functions in D dimensions, PNAS.
Slepian & Eisenstein, Accelerating the two-point and three-point galaxy correlation functions using Fourier transforms, MNRASL.
Slepian & Eisenstein, Computing the three-point correlation function of galaxies in O(N2) time, MNRAS.
Realizing a Density Field with Given N-Point Correlations
Slepian, Algorithm to produce a density field with given two-, three-, and four-point correlation functions, RAS Techniques and Instruments. On arXiv here.
Improving the Line of Sight Used in 2- and 3-Point Statistics
Philcox & Slepian, Beyond the Yamamoto approximation: Anisotropic power spectra and correlation functions with pairwise lines of sight, PRD.
Garcia & Slepian, Improving the line of sight for the anisotropic 3-point correlation function of galaxies: Centroid and Unit-Vector-Average methods scaling as 𝒪 (N2), MNRAS.
Hand, Li, Slepian, & Seljak, An optimal FFT-based anisotropic power spectrum estimator, JCAP.
Slepian & Eisenstein, A new look at lines of sight: using Fourier methods for the wide-angle anisotropic 2-point correlation function, in submission.
Slepian & Eisenstein, Accelerating the two-point and three-point galaxy correlation functions using Fourier transforms, MNRASL (introduced idea of using spherical harmonic decomposition to compute 2PCF in Yamamoto approximation wherein one of the two pair members defines the line of sight).
General Purpose Cosmology
Hand, Feng, Beutler, Li, Modi, Seljak, & Slepian, nbodykit: an open-source, massively parallel toolkit for large-scale structure, The Astronomical Journal.
Calculation of the Nonlinear Scale and Mass
Krolewski & Slepian, Accelerating computation of the density-field filtering scale σ(R) and non-linear mass by an order of magnitude, MNRAS.
Baryon Acoustic Oscillation Scale Fitting
Hansen & Slepian, Accelerating BAO scale fitting using Taylor series, MNRAS.
Multiple Spherical Bessel Function Integrals of the Power Spectrum
Slepian, Li, Schmittfull & Vlah, Rotation method for accelerating multiple-spherical Bessel function integrals against a numerical source function, in submission.
2-Loop Perturbation Theory
Slepian, On decoupling the integrals of cosmological perturbation theory, MNRAS.
Spherical Collapse and the Kepler Problem
Slepian & Philcox, A uniform spherical goat (problem): explicit solution for homologous collapse's radial evolution in time, MNRASL.
Philcox, Goodman, & Slepian, Kepler’s Goat Herd: An exact solution to Kepler’s equation for elliptical orbits, MNRAS.
Mathematical Methods
Mathematical Methods
We have pursued improvements to the math available for cosmology where needed.
We have pursued improvements to the math available for cosmology where needed.
Isotropic Basis Functions
Cahn & Slepian, Isotropic N-point basis functions and their properties, Journal of Physics A: Mathematical and Theoretical. On arXiv here.
Slepian, Chellino, Hou, & Greco, On a generating function for the isotropic basis functions and other connected results, Journal of Physics A: Mathematical and Theoretical. On arXiv here.
2-Loop Perturbation Theory
Slepian, On decoupling the integrals of cosmological perturbation theory, MNRAS. On arXiv here.
Spherical Bessel Function Integrals
Chellino & Slepian, Triple-spherical Bessel function integrals with exponential and Gaussian damping: towards an analytic N-point correlation function covariance model, PRSA. On arXiv here.
Meigs & Slepian, On a General Method for Resolving Integrals of Multiple Spherical Bessel Functions Against Power Laws into Distributions, in submission.
Philcox & Slepian, An exact integral-to-sum relation for products of Bessel functions, PRSA. On arXiv here.
Star Formation
Star Formation
We have broken new ground in applying higher-order correlations to the physics underlying star formation, as well as building analytic models to understand the impact of environment on a collapsing pre-stellar gas cloud; currently we also are at work on projects with VISTA Magellanic Cloud (VMC) survey data.
We have broken new ground in applying higher-order correlations to the physics underlying star formation, as well as building analytic models to understand the impact of environment on a collapsing pre-stellar gas cloud; currently we also are at work on projects with VISTA Magellanic Cloud (VMC) survey data.
4-Point Correlation Function of MHD Turbulence Simulations
Williamson, Sunseri, Slepian, Hou & Greco, First Measurements of the 4-Point Correlation Function of Magnetohydrodynamic Turbulence as a Novel Probe of the Interstellar Medium, in submission.
3-Point Correlation Function & Wavelet Scattering Transform Studies of MHD Turbulence Simulations
Portillo, Slepian, Burkhart, Kahraman, & Finkbeiner, Developing the 3-point Correlation Function for the Turbulent Interstellar Medium, ApJ. On arXiv here.
Saydjari, Portillo, Slepian, Kahraman, Burkhart & Finkbeiner, Classification of Magnetohydrodynamic Simulations using Wavelet Scattering Transforms, ApJ. On arXiv here.
Burkhart et al. incl. Slepian, The Catalogue for Astrophysical Turbulence Simulations (CATS), ApJ. On arXiv here.
Analytic Model of Collapse of a Core in a Filament
Slepian & Cahn, An idealized model for collapse of a molecular core within a filament, MNRAS.
VMC Data Projects
Miller, Slepian, Lada, de Grijs, Cioni, Krumholz et al., An automated method to detect and characterise semi-resolved star clusters, in submission.
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