A Faster Fourier Transform? Computing Small-Scale Power Spectra and Bispectra for Cosmological Simulations in $\mathcal{O}(N^2)$ Time

Abstract

We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales, requiring orders of magnitude less computation time than Fast Fourier Transform based approaches alone. These methods are applicable to any tracer; simulation particles, halos or galaxies, and take advantage of the simple geometry of the box and periodicity to remove almost all dependence on large random particle catalogs. By working in configuration-space, both power spectra and bispectra can be computed via a weighted sum of particle pairs up to some radius, which can be reduced at larger $k$, leading to algorithms with decreasing complexity on small scales. These do not suffer from aliasing or shot-noise, allowing spectra to be computed to arbitrarily large wavenumbers. The estimators are rigorously derived and tested against simulations, and their covariances discussed. The accompanying code, HIPSTER, has been publicly released, incorporating these algorithms. Such estimators will be of great use in the analysis of large sets of high-resolution simulations.

31 pages, 6 figures, accepted by MNRAS. Code available at https://HIPSTER.readthedocs.io

References in corpus (12)

• Cosmological Constraints from the SDSS Luminous Red Galaxies
• Astrophysics Source Code Library
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in Fourier-space
• Cosmology and the Bispectrum
• The Weak Lensing Signal and the Clustering of BOSS Galaxies II: Astrophysical and Cosmological Constraints
• Testing general relativity with the multipole spectra of the SDSS luminous red galaxies
• Estimating Covariance Matrices for Two- and Three-Point Correlation Function Moments in Arbitrary Survey Geometries
• Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in Configuration-Space
• Tau flavored dark matter and its impact on tau Yukawa coupling
• Computing 3 point correlation function randoms counts without the randoms catalogue
• Rotation method for accelerating multiple-spherical Bessel function integrals against a numerical source function
• Advancing the matter bispectrum estimation of large-scale structure: a comparison of dark matter codes

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• Cosmology with cosmic web environments I. Real-space power spectra
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• Modeling the Marked Spectrum of Matter and Biased Tracers in Real- and Redshift-Space
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• An Exact Integral-to-Sum Relation for Products of Bessel Functions
• Predictive uncertainty on improved astrophysics recovery from multifield cosmology
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