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

Journal Article · · Physical Review D
 [1];  [2]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Berkeley Center for Cosmological Physics, Dept. of Physics; Inst. for Advanced Study, Princeton, NJ (United States)
  2. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics and Dept. of Physics; Stanford Univ., CA (United States). Kavli Inst. for Particle Astrophysics and Cosmology; SLAC National Accelerator Lab., Menlo Park, CA (United States)
+ Show Author Affiliations

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. Here, 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 fast fourier transform perturbation theory 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.

Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC02-76SF00515
OSTI ID:
1360171
Journal Information:
Physical Review D, Journal Name: Physical Review D Journal Issue: 10 Vol. 94; ISSN PRVDAQ; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (104)

The effective field theory of cosmological large scale structures journal September 2012
Large-scale structure of the Universe and cosmological perturbation theory journal September 2002
Cuba—a library for multidimensional numerical integration journal June 2005
Cuba—a library for multidimensional numerical integration journal June 2007
Uncorrelated modes of the non-linear power spectrum journal February 2000
Coupling of modes of cosmological mass density fluctuations journal December 1986
Second-order power spectrum and nonlinear evolution at high redshift journal August 1994
Loop Corrections in Nonlinear Cosmological Perturbation Theory. II. Two‐Point Statistics and Self‐Similarity journal December 1996
Loop Corrections in Nonlinear Cosmological Perturbation Theory journal July 1996
Measuring Primordial Non‐Gaussianity in the Cosmic Microwave Background journal November 2005
Perturbation Theory Reloaded: Analytical Calculation of Nonlinearity in Baryonic Oscillations in the Real‐Space Matter Power Spectrum journal November 2006
Nonlinear Behavior of Baryon Acoustic Oscillations from the Zel'Dovich Approximation Using a Non-Fourier Perturbation Approach journal May 2012
Flowing with time: a new approach to non-linear cosmological perturbations journal October 2008
Non-linear power spectrum including massive neutrinos: the time-RG flow approach journal June 2009
Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS journal August 2009
Distribution function approach to redshift space distortions journal November 2011
Coarse-grained cosmological perturbation theory journal January 2012
Distribution function approach to redshift space distortions. Part II: N -body simulations journal February 2012
Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering journal June 2012
Cosmological non-linearities as an effective fluid journal July 2012
Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter journal November 2012
Distribution function approach to redshift space distortions. Part III: halos and galaxies journal November 2012
On the renormalization of the effective field theory of large scale structures journal August 2013
On the non-linear scale of cosmological perturbation theory journal September 2013
Distribution function approach to redshift space distortions. Part V: perturbation theory applied to dark matter halos journal October 2013
On the velocity in the Effective Field Theory of Large Scale Structures journal March 2014
Peculiar velocities in redshift space: formalism, N-body simulations and perturbation theory journal May 2014
The Lagrangian-space Effective Field Theory of large scale structures journal May 2014
The 2-loop matter power spectrum and the IR-safe integrand journal July 2014
The Effective Field Theory of Large Scale Structures at two loops journal July 2014
A coarse grained perturbation theory for the Large Scale Structure, with cosmology and time independence in the UV journal September 2014
The IR-resummed Effective Field Theory of Large Scale Structures journal February 2015
A Lagrangian effective field theory journal September 2015
Cosmological perturbation theory in 1+1 dimensions journal January 2016
Perturbation theory, effective field theory, and oscillations in the power spectrum journal March 2016
FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory journal September 2016
A Critique of Rees's Theory of Primordial Gravitational Radiation journal February 1972
Clustering in real space and in redshift space journal July 1987
Non-linear evolution of the angular momentum of protostructures from tidal torques journal September 1996
Convolution Lagrangian perturbation theory for biased tracers journal December 2012
On the signature of the baryon–dark matter relative velocity in the two- and three-point galaxy correlation functions journal February 2015
Computing the three-point correlation function of galaxies in $\mathcal {O}(N^2)$ time journal October 2015
Redshift-space distortions, pairwise velocities, and nonlinearities journal October 2004
Renormalized cosmological perturbation theory journal March 2006
Resumming cosmological perturbations via the Lagrangian picture: One-loop results in real space and in redshift space journal March 2008
Multipoint propagators in cosmological gravitational instability journal November 2008
General CMB and primordial bispectrum estimation: Mode expansion, map making, and measures of F NL journal July 2010
Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory journal September 2010
Relative velocity of dark matter and baryonic fluids and the formation of the first structures journal October 2010
Linear power spectrum of observed source number counts journal August 2011
Shift of the baryon acoustic oscillation scale: A simple physical picture journal May 2012
Constructing regularized cosmic propagators journal June 2012
Rapid separable analysis of higher order correlators in large-scale structure journal September 2012
Direct and fast calculation of regularized cosmological power spectrum at two-loop order journal November 2012
Universal non-Gaussian initial conditions for N -body simulations journal December 2012
Fast estimation of gravitational and primordial bispectra in large scale structures journal September 2013
Consistent effective theory of long-wavelength cosmological perturbations journal July 2014
Integrated perturbation theory and one-loop power spectra of biased tracers journal August 2014
Lagrangian perturbation theory at one loop order: Successes, failures, and improvements journal January 2015
Near optimal bispectrum estimators for large-scale structure journal February 2015
Halo Zel’dovich model and perturbation theory: Dark matter power spectrum and correlation function journal June 2015
Eulerian BAO reconstructions and N -point statistics journal December 2015
Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms journal May 2016
Constructing perturbation theory kernels for large-scale structure in generalized cosmologies journal July 2016
Bias to CMB lensing measurements from the bispectrum of large-scale structure journal August 2016
Nonlinear fields in generalized cosmologies journal September 2016
Towards an accurate model of the redshift-space clustering of haloes in the quasi-linear regime: Redshift-space distortions journal August 2011
MPTbreeze : a fast renormalized perturbative scheme: MPTbreeze journal November 2012
Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe journal September 2008
On the non-linear scale of cosmological perturbation theory text January 2013
The Sdss-Iv Extended Baryon Oscillation Spectroscopic Survey: Overview and Early data journal February 2016
Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space text January 2007
Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations text January 2008
Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe text January 2008
Non-linear Power Spectrum including Massive Neutrinos: the Time-RG Flow Approach text January 2009
Cosmological Non-Linearities as an Effective Fluid text January 2010
Relative velocity of dark matter and baryonic fluids and the formation of the first structures text January 2010
Distribution function approach to redshift space distortions. Part II: N-body simulations text January 2011
Nonlinear Behavior of Baryon Acoustic Oscillations from the Zel'dovich Approximation Using a Non-Fourier Perturbation Approach text January 2012
The Effective Field Theory of Cosmological Large Scale Structures text January 2012
Convolution Lagrangian perturbation theory for biased tracers text January 2012
Distribution function approach to redshift space distortions. Part V: perturbation theory applied to dark matter halos text January 2013
The Lagrangian-space Effective Field Theory of Large Scale Structures text January 2013
The IR-resummed Effective Field Theory of Large Scale Structures text January 2014
A coarse grained perturbation theory for the Large Scale Structure, with cosmology and time independence in the UV text January 2014
Lagrangian perturbation theory at one loop order: successes, failures, and improvements text January 2014
On the signature of the baryon-dark matter relative velocity in the two and three-point galaxy correlation functions text January 2014
Near optimal bispectrum estimators for large-scale structure text January 2014
Halo Zeldovich model and perturbation theory: dark matter power spectrum and correlation function text January 2015
A Lagrangian effective field theory text January 2015
The SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Overview and Early Data text January 2015
Perturbation theory, effective field theory, and oscillations in the power spectrum text January 2015
FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory text January 2016
A bias to CMB lensing measurements from the bispectrum of large-scale structure text January 2016
Large-Scale Structure of the Universe and Cosmological Perturbation Theory text January 2001
Measuring primordial non-Gaussianity in the cosmic microwave background text January 2003
Renormalized Cosmological Perturbation Theory text January 2005
Loop Corrections in Non-Linear Cosmological Perturbation Theory text January 1995
Uncorrelated Modes of the Nonlinear Power Spectrum text January 1999
Distribution function approach to redshift space distortions text January 2011
Distribution function approach to redshift space distortions. Part III: halos and galaxies text January 2012
Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter text January 2012
Distribution function approach to redshift space distortions. Part II:N-body simulations text January 2012
Distribution function approach to redshift space distortions. Part V: perturbation theory applied to dark matter halos text January 2013

Cited By (10)

FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory journal February 2017
The matter power spectrum in redshift space using effective field theory journal November 2017
Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals journal April 2018
Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error journal November 2019
Velocity bias and the nonlinear perturbation theory of peaks journal October 2019
Perturbation theory challenge for cosmological parameters estimation: Matter power spectrum in real space journal March 2019
FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory text January 2016
The matter power spectrum in redshift space using effective field theory text January 2017
Cosmological Perturbation Theory Using the FFTLog: Formalism and Connection to QFT Loop Integrals text January 2017
Velocity bias and the nonlinear perturbation theory of peaks text January 2019

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS