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Title: The 2-loop matter power spectrum and the IR-safe integrand

Journal Article · · Journal of Cosmology and Astroparticle Physics
 [1];  [2];  [2];  [3]
  1. Stanford Univ., Stanford, CA (United States)
  2. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
  3. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States); European Organization for Nuclear Research (CERN), Geneva (Switzerland)
+ Show Author Affiliations

Large scale structure surveys are likely the next leading probe of cosmological information. It is therefore crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a manifestly convergent perturbation theory for the weakly non-linear regime, where dark matter correlation functions are computed in an expansion of the wavenumber k over the wavenumber associated to the non-linear scale kNL. To push the predictions to higher wavenumbers, it is necessary to compute the 2-loop matter power spectrum. For equal-time correlators, exactly as with standard perturturbation theory, there are IR divergences present in each diagram that cancel completely in the final result. We develop a method by which all 2-loop diagrams are computed as one integral, with an integrand that is manifestly free of any IR divergences. This allows us to compute the 2-loop power spectra in a reliable way that is much less numerically challenging than standard techniques. We apply our method to scaling universes where the linear power spectrum is a single power law of k, and where IR divergences can particularly easily interfere with accurate evaluation of loop corrections if not handled carefully. In conclusion, we show that our results are independent of IR cutoff and, after renormalization, of the UV cutoff, and comment how the method presented here naturally generalizes to higher loops.

Research Organization:
Stanford Univ., CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0008078
OSTI ID:
1491159
Journal Information:
Journal of Cosmology and Astroparticle Physics, Vol. 2014, Issue 07; ISSN 1475-7516
Publisher:
Institute of Physics (IOP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 77 works
Citation information provided by
Web of Science

References (22)

Cosmological non-linearities as an effective fluid journal July 2012
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
Critical look at cosmological perturbation theory techniques journal August 2009
On the renormalization of the effective field theory of large scale structures journal August 2013
Generation of vorticity and velocity dispersion by orbit crossing journal August 2009
Self-similar Evolution of Gravitational Clustering: Is N = -1 Special? journal January 1996
Loop Corrections in Nonlinear Cosmological Perturbation Theory journal July 1996
Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure journal May 2013
Direct and fast calculation of regularized cosmological power spectrum at two-loop order journal November 2012
Coupling of modes of cosmological mass density fluctuations journal December 1986
Cuba—a library for multidimensional numerical integration journal June 2005
On the non-linear scale of cosmological perturbation theory journal September 2013
Cuba—a library for multidimensional numerical integration journal June 2007
On the non-linear scale of cosmological perturbation theory text January 2013
Generation of Vorticity and Velocity Dispersion by Orbit Crossing text January 2008
A critical look at cosmological perturbation theory techniques text January 2009
Cosmological Non-Linearities as an Effective Fluid text January 2010
The Effective Field Theory of Cosmological Large Scale Structures text January 2012
Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure text January 2013
Large-Scale Structure of the Universe and Cosmological Perturbation Theory text January 2001
Loop Corrections in Non-Linear Cosmological Perturbation Theory text January 1995

Cited By (42)

Structure formation with massive neutrinos: going beyond linear theory journal November 2014
The IR-resummed Effective Field Theory of Large Scale Structures journal February 2015
The bispectrum in the Effective Field Theory of Large Scale Structure journal May 2015
Analytic prediction of baryonic effects from the EFT of large scale structures journal May 2015
The one-loop matter bispectrum in the Effective Field Theory of Large Scale Structures journal October 2015
Effective theory of large-scale structure with primordial non-Gaussianity journal November 2015
Cosmological perturbation theory in 1+1 dimensions journal January 2016
On the reach of perturbative descriptions for dark matter displacement fields journal March 2016
Precision comparison of the power spectrum in the EFTofLSS with simulations journal May 2016
The trispectrum in the Effective Field Theory of Large Scale Structure journal June 2016
Time-sliced perturbation theory for large scale structure I: general formalism journal July 2016
Principal shapes and squeezed limits in the effective field theory of large scale structure journal November 2016
Efficient exploration of cosmology dependence in the EFT of LSS journal April 2017
The matter power spectrum in redshift space using effective field theory journal November 2017
Dark energy and modified gravity in the Effective Field Theory of Large-Scale Structure journal April 2018
Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals journal April 2018
Lensing reconstruction from line intensity maps: the impact of gravitational nonlinearity journal July 2018
Infrared resummation for biased tracers in redshift space journal July 2018
The effective field theory of large scale structure at three loops journal November 2019
Matter bispectrum of large-scale structure: Three-dimensional comparison between theoretical models and numerical simulations journal April 2016
Non-Gaussian covariance of the matter power spectrum in the effective field theory of large scale structure journal June 2016
Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals journal November 2016
EFT of large scale structures in redshift space journal March 2018
On the soft limit of the large scale structure power spectrum: UV dependence text January 2015
The Hunt for Primordial Interactions in the Large-Scale Structures of the Universe journal August 2019
On the soft limit of the large scale structure power spectrum: UV dependence journal November 2015
The effective field theory of large scale structure at three loops text January 2019
The Effective Field Theory of Large Scale Structure at Three Loops text January 2019
The IR-resummed Effective Field Theory of Large Scale Structures text January 2014
The One-Loop Matter Bispectrum in the Effective Field Theory of Large Scale Structures text January 2014
Lagrangian perturbation theory at one loop order: successes, failures, and improvements text January 2014
The Effective Field Theory of Large Scale Structure at Two Loops: the apparent scale dependence of the speed of sound text January 2015
Precision Comparison of the Power Spectrum in the EFTofLSS with Simulations text January 2015
Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism text January 2015
Principal Shapes and Squeezed Limits in the Effective Field Theory of Large Scale Structure text January 2016
FFT-PT: Reducing the two-loop large-scale structure power spectrum to low-dimensional radial integrals 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
Dark Energy and Modified Gravity in the Effective Field Theory of Large-Scale Structure text January 2017
Infrared Resummation for Biased Tracers in Redshift Space text January 2018
Numerical and Perturbative Computations of the Fuzzy Dark Matter Model text January 2018
The Effective Field Theory of Large Scale Structure at Three Loops text January 2019

Figures / Tables (7)

Figure 1(p. 18)figure Figure 1
Figure 2(p. 19)figure Figure 2
Figure 3(p. 20)figure Figure 3
Figure 4(p. 23)figure Figure 4
Figure 5(p. 24)figure Figure 5
Figure 6(p. 25)figure Figure 6
Figure 7(p. 26)figure Figure 7

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Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
power spectrum
cosmological perturbation theory