FFT-PT: Reducing the two-loop large-scale structure power spectrum to low-dimensional radial integrals

Abstract

Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve this is to model nonlinear scales perturbatively. Unfortunately, this involves high-dimensional loop integrals that are cumbersome to evaluate. Trying to simplify this, we show how two-loop (next-to-next-to-leading order) corrections to the density power spectrum can be reduced to low-dimensional, radial integrals. Many of those can be evaluated with a one-dimensional Fast Fourier Transform, which is significantly faster than the five-dimensional Monte-Carlo integrals that are needed otherwise. The general idea of this FFT-PT method is to switch between Fourier and position space to avoid convolutions and integrate over orientations, leaving only radial integrals. This reformulation is independent of the underlying shape of the initial linear density power spectrum and should easily accommodate features such as those from baryonic acoustic oscillations. We also discuss how to account for halo bias and redshift space distortions.

13+11 pages, updated discussion of multiple inverse Laplacians

References in corpus (67)

• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Cuba - a library for multidimensional numerical integration
• The SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Overview and Early Data
• Cosmological Non-Linearities as an Effective Fluid
• The Effective Field Theory of Cosmological Large Scale Structures
• Redshift-Space Distortions, Pairwise Velocities and Nonlinearities
• Renormalized Cosmological Perturbation Theory
• The linear power spectrum of observed source number counts
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• Fingers of God
• Relative velocity of dark matter and baryonic fluids and the formation of the first structures
• Baryon Acoustic Oscillations in 2D: Modeling Redshift-space Power Spectrum from Perturbation Theory
• Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
• Uncorrelated Modes of the Nonlinear Power Spectrum
• Measuring primordial non-Gaussianity in the cosmic microwave background
• Second Order Power Spectrum and Nonlinear Evolution at High Redshift
• The IR-resummed Effective Field Theory of Large Scale Structures
• Towards an accurate model of the redshift space clustering of halos in the quasilinear regime
• Convolution Lagrangian perturbation theory for biased tracers
• The Lagrangian-space Effective Field Theory of Large Scale Structures
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• Loop Corrections in Non-Linear Cosmological Perturbation Theory
• Perturbation Theory Reloaded: Analytical Calculation of Non-linearity in Baryonic Oscillations in the Real Space Matter Power Spectrum
• RegPT: Direct and fast calculation of regularized cosmological power spectrum at two-loop order
• The Effective Field Theory of Large Scale Structures at Two Loops
• Multi-Point Propagators in Cosmological Gravitational Instability
• On the Renormalization of the Effective Field Theory of Large Scale Structures
• A Lagrangian effective field theory
• General CMB and Primordial Bispectrum Estimation I: Mode Expansion, Map-Making and Measures of f_NL
• FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory
• Perturbation theory, effective field theory, and oscillations in the power spectrum
• The Shift of the Baryon Acoustic Oscillation Scale: A Simple Physical Picture
• Loop Corrections in Non-Linear Cosmological Perturbation Theory II. Two-point Statistics and Self-Similarity
• A Consistent Effective Theory of Long-Wavelength Cosmological Perturbations
• Non-linear Power Spectrum including Massive Neutrinos: the Time-RG Flow Approach
• The 2-loop matter power spectrum and the IR-safe integrand
• Computing the Three-Point Correlation Function of Galaxies in $\mathcal{O}(N^2)$ Time
• Non-linear evolution of the angular momentum of protostructures from tidal torques
• On the Velocity in the Effective Field Theory of Large Scale Structures
• Distribution function approach to redshift space distortions
• Eulerian BAO Reconstructions and N-Point Statistics
• Coarse-Grained Cosmological Perturbation Theory
• Fast Large Scale Structure Perturbation Theory using 1D FFTs
• Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering
• Cosmological perturbation theory in 1+1 dimensions
• Near optimal bispectrum estimators for large-scale structure
• Lagrangian perturbation theory at one loop order: successes, failures, and improvements
• Constructing Regularized Cosmic Propagators
• Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe
• MPTbreeze: A fast renormalized perturbative scheme
• On the non-linear scale of cosmological perturbation theory
• Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter
• A bias to CMB lensing measurements from the bispectrum of large-scale structure
• Distribution function approach to redshift space distortions. Part II: N-body simulations
• Distribution function approach to redshift space distortions, Part III: halos and galaxies
• On the signature of the baryon-dark matter relative velocity in the two and three-point galaxy correlation functions
• Rapid Separable Analysis of Higher Order Correlators in Large Scale Structure
• Peculiar velocities in redshift space: formalism, N-body simulations and perturbation theory
• Distribution function approach to redshift space distortions. Part V: perturbation theory applied to dark matter halos
• Non-linear Fields in Generalized Cosmologies
• Halo Zeldovich model and perturbation theory: dark matter power spectrum and correlation function
• Fast Estimation of Gravitational and Primordial Bispectra in Large Scale Structures
• Constructing perturbation theory kernels for large-scale structure in generalized cosmologies
• Integrated Perturbation Theory and One-loop Power Spectra of Biased Tracers
• Universal Non-Gaussian Initial Conditions for N-body Simulations
• A coarse grained perturbation theory for the Large Scale Structure, with cosmology and time independence in the UV
• Nonlinear Behavior of Baryon Acoustic Oscillations from the Zel'dovich Approximation Using a Non-Fourier Perturbation Approach

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• Non-linear perturbation theory extension of the Boltzmann code CLASS
• Consistent Modeling of Velocity Statistics and Redshift-Space Distortions in One-Loop Perturbation Theory
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• Cosmological Perturbation Theory Using the FFTLog: Formalism and Connection to QFT Loop Integrals
• Beyond Limber: Efficient computation of angular power spectra for galaxy clustering and weak lensing
• The Galaxy Power Spectrum and Bispectrum in Redshift Space
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• FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory
• An analytic implementation of the IR-resummation for the BAO peak
• The matter power spectrum in redshift space using effective field theory
• Fast computation of non-linear power spectrum in cosmologies with massive neutrinos
• The one-loop matter bispectrum as a probe of gravity and dark energy
• Clustering in Massive Neutrino Cosmologies via Eulerian Perturbation Theory
• Large-scale structure perturbation theory without losing stream crossing
• Perturbation theory challenge for cosmological parameters estimation: Matter power spectrum in real space
• Precise and Accurate Cosmology with CMBxLSS Power Spectra and Bispectra
• Weakly non-Gaussian formula for the Minkowski functionals in general dimensions
• Cosmological Angular Trispectra and Non-Gaussian Covariance
• fkPT: Constraining scale-dependent modified gravity with the full-shape galaxy power spectrum
• Modelling the next-to-leading order matter three-point correlation function using FFTLog
• On the asymptotic connection between full- and flat-sky angular correlators
• Integrated perturbation theory for cosmological tensor fields. I. Basic formulation
• The statistics of peaks of weakly non-Gaussian random fields: Effects of bispectrum in two- and three-dimensions
• Integrated perturbation theory for cosmological tensor fields. III. Projection effects
• Integrated perturbation theory for cosmological tensor fields. II. Loop corrections
• Perturbation Theory Remixed: Improved Nonlinearity Modeling beyond Standard Perturbation Theory
• Fast Calculation of Nonlinear Redshift-space Galaxy Power Spectrum Including Selection Bias
• Flat-sky Angular Power Spectra Revisited
• Triple-Spherical Bessel Function Integrals with Exponential and Gaussian Damping: Towards an Analytic N-Point Correlation Function Covariance Model
• Velocity bias and the nonlinear perturbation theory of peaks
• The large-separation expansion of peak clustering in Gaussian random fields
• Perturbation theory challenge for cosmological parameters estimation II.: Matter power spectrum in redshift space
• Implementing spectra response function approaches for fast calculation of power spectra and bispectra