The Effective Field Theory of Large Scale Structures at two loops
Abstract
Here, large scale structure surveys promise to be 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 of dark matter, where correlation functions are computed in an expansion of the wavenumber k of a mode over the wavenumber associated with the non-linear scale kNL. Since most of the information is contained at high wavenumbers, it is necessary to compute higher order corrections to correlation functions. After the one-loop correction to the matter power spectrum, we estimate that the next leading one is the two-loop contribution, which we compute here. At this order in k/kNL, there is only one counterterm in the EFTofLSS that must be included, though this term contributes both at tree-level and in several one-loop diagrams. We also discuss correlation functions involving the velocity and momentum fields. We find that the EFTofLSS prediction at two loops matches to percent accuracy the non-linear matter power spectrum at redshift zero up to k~ 0.6 h Mpc–1, requiring just one unknown coefficient that needs to be fit to observations. Given that Standard Perturbation Theorymore »
- Authors:
-
- Stanford Univ., Stanford, CA (United States)
- Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States); European Organization for Nuclear Research (CERN), Geneva (Switzerland)
- Publication Date:
- Research Org.:
- Stanford Univ., CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1491160
- Grant/Contract Number:
- SC0008078
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Cosmology and Astroparticle Physics
- Additional Journal Information:
- Journal Volume: 2014; Journal Issue: 07; Journal ID: ISSN 1475-7516
- Publisher:
- Institute of Physics (IOP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; power spectrum; cosmological perturbation theory
Citation Formats
Carrasco, John Joseph M., Foreman, Simon, Green, Daniel, and Senatore, Leonardo. The Effective Field Theory of Large Scale Structures at two loops. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/07/057.
Carrasco, John Joseph M., Foreman, Simon, Green, Daniel, & Senatore, Leonardo. The Effective Field Theory of Large Scale Structures at two loops. United States. https://doi.org/10.1088/1475-7516/2014/07/057
Carrasco, John Joseph M., Foreman, Simon, Green, Daniel, and Senatore, Leonardo. Thu .
"The Effective Field Theory of Large Scale Structures at two loops". United States. https://doi.org/10.1088/1475-7516/2014/07/057. https://www.osti.gov/servlets/purl/1491160.
@article{osti_1491160,
title = {The Effective Field Theory of Large Scale Structures at two loops},
author = {Carrasco, John Joseph M. and Foreman, Simon and Green, Daniel and Senatore, Leonardo},
abstractNote = {Here, large scale structure surveys promise to be 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 of dark matter, where correlation functions are computed in an expansion of the wavenumber k of a mode over the wavenumber associated with the non-linear scale kNL. Since most of the information is contained at high wavenumbers, it is necessary to compute higher order corrections to correlation functions. After the one-loop correction to the matter power spectrum, we estimate that the next leading one is the two-loop contribution, which we compute here. At this order in k/kNL, there is only one counterterm in the EFTofLSS that must be included, though this term contributes both at tree-level and in several one-loop diagrams. We also discuss correlation functions involving the velocity and momentum fields. We find that the EFTofLSS prediction at two loops matches to percent accuracy the non-linear matter power spectrum at redshift zero up to k~ 0.6 h Mpc–1, requiring just one unknown coefficient that needs to be fit to observations. Given that Standard Perturbation Theory stops converging at redshift zero at k~ 0.1 h Mpc–1, our results demonstrate the possibility of accessing a factor of order 200 more dark matter quasi-linear modes than naively expected. If the remaining observational challenges to accessing these modes can be addressed with similar success, our results show that there is tremendous potential for large scale structure surveys to explore the primordial universe.},
doi = {10.1088/1475-7516/2014/07/057},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 07,
volume = 2014,
place = {United States},
year = {Thu Jul 31 00:00:00 EDT 2014},
month = {Thu Jul 31 00:00:00 EDT 2014}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 114 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Cosmological non-linearities as an effective fluid
journal, July 2012
- Baumann, Daniel; Nicolis, Alberto; Senatore, Leonardo
- Journal of Cosmology and Astroparticle Physics, Vol. 2012, Issue 07
The effective field theory of cosmological large scale structures
journal, September 2012
- Carrasco, John Joseph M.; Hertzberg, Mark P.; Senatore, Leonardo
- Journal of High Energy Physics, Vol. 2012, Issue 9
Large-scale structure of the Universe and cosmological perturbation theory
journal, September 2002
- Bernardeau, F.; Colombi, S.; Gaztañaga, E.
- Physics Reports, Vol. 367, Issue 1-3
Renormalized cosmological perturbation theory
journal, March 2006
- Crocce, Martín; Scoccimarro, Román
- Physical Review D, Vol. 73, Issue 6
Critical look at cosmological perturbation theory techniques
journal, August 2009
- Carlson, Jordan; White, Martin; Padmanabhan, Nikhil
- Physical Review D, Vol. 80, Issue 4
On the renormalization of the effective field theory of large scale structures
journal, August 2013
- Pajer, Enrico; Zaldarriaga, Matias
- Journal of Cosmology and Astroparticle Physics, Vol. 2013, Issue 08
Contributions to the dark matter 3-Point function from the radiation era
journal, May 2010
- Fitzpatrick, A. Liam; Senatore, Leonardo; Zaldarriaga, Matias
- Journal of Cosmology and Astroparticle Physics, Vol. 2010, Issue 05
Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann‐Robertson‐Walker Models
journal, August 2000
- Lewis, Antony; Challinor, Anthony; Lasenby, Anthony
- The Astrophysical Journal, Vol. 538, Issue 2
Self-similar Evolution of Gravitational Clustering: Is N = -1 Special?
journal, January 1996
- Jain, Bhuvnesh; Bertschinger, Edmund
- The Astrophysical Journal, Vol. 456
Loop Corrections in Nonlinear Cosmological Perturbation Theory
journal, July 1996
- Scoccimarro, Roman; Frieman, Joshua
- The Astrophysical Journal Supplement Series, Vol. 105
Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure
journal, May 2013
- Peloso, Marco; Pietroni, Massimo
- Journal of Cosmology and Astroparticle Physics, Vol. 2013, Issue 05
Symmetries and consistency relations in the large scale structure of the universe
journal, August 2013
- Kehagias, A.; Riotto, A.
- Nuclear Physics B, Vol. 873, Issue 3
Resummed propagators in multicomponent cosmic fluids with the eikonal approximation
journal, March 2012
- Bernardeau, Francis; Van de Rijt, Nicolas; Vernizzi, Filippo
- Physical Review D, Vol. 85, Issue 6
Nonlinear power spectrum from resummed perturbation theory: a leap beyond the BAO scale
journal, December 2012
- Anselmi, Stefano; Pietroni, Massimo
- Journal of Cosmology and Astroparticle Physics, Vol. 2012, Issue 12
On the non-linear scale of cosmological perturbation theory
journal, September 2013
- Blas, Diego; Garny, Mathias; Konstandin, Thomas
- Journal of Cosmology and Astroparticle Physics, Vol. 2013, Issue 09
Coupling of modes of cosmological mass density fluctuations
journal, December 1986
- Goroff, M. H.; Grinstein, B.; Rey, S. -J.
- The Astrophysical Journal, Vol. 311
The Coyote Universe. i. Precision Determination of the Nonlinear Matter Power Spectrum
journal, April 2010
- Heitmann, Katrin; White, Martin; Wagner, Christian
- The Astrophysical Journal, Vol. 715, Issue 1
The Coyote Universe. ii. Cosmological Models and Precision Emulation of the Nonlinear Matter Power Spectrum
journal, October 2009
- Heitmann, Katrin; Higdon, David; White, Martin
- The Astrophysical Journal, Vol. 705, Issue 1
The Coyote Universe. iii. Simulation Suite and Precision Emulator for the Nonlinear Matter Power Spectrum
journal, April 2010
- Lawrence, Earl; Heitmann, Katrin; White, Martin
- The Astrophysical Journal, Vol. 713, Issue 2
The Coyote Universe Extended: Precision Emulation of the Matter Power Spectrum
journal, December 2013
- Heitmann, Katrin; Lawrence, Earl; Kwan, Juliana
- The Astrophysical Journal, Vol. 780, Issue 1
Cuba—a library for multidimensional numerical integration
journal, June 2005
- Hahn, T.
- Computer Physics Communications, Vol. 168, Issue 2
On the velocity in the Effective Field Theory of Large Scale Structures
journal, March 2014
- Mercolli, Lorenzo; Pajer, Enrico
- Journal of Cosmology and Astroparticle Physics, Vol. 2014, Issue 03
Distribution function approach to redshift space distortions. Part II: N -body simulations
journal, February 2012
- Okumura, Teppei; Seljak, Uroš; McDonald, Patrick
- Journal of Cosmology and Astroparticle Physics, Vol. 2012, Issue 02
Generation of vorticity and velocity dispersion by orbit crossing
journal, August 2009
- Pueblas, Sebastián; Scoccimarro, Román
- Physical Review D, Vol. 80, Issue 4
Limits on non-Gaussianities from WMAP data
journal, May 2006
- Creminelli, Paolo; Nicolis, Alberto; Senatore, Leonardo
- Journal of Cosmology and Astroparticle Physics, Vol. 2006, Issue 05
Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data
journal, January 2010
- Senatore, Leonardo; Smith, Kendrick M.; Zaldarriaga, Matias
- Journal of Cosmology and Astroparticle Physics, Vol. 2010, Issue 01
Constraining running non-gaussianity
journal, December 2009
- Sefusatti, Emiliano; Liguori, Michele; Yadav, Amit P. S.
- Journal of Cosmology and Astroparticle Physics, Vol. 2009, Issue 12
The effective field theory of inflation
journal, March 2008
- Cheung, Clifford; Fitzpatrick, A. Liam; Kaplan, Jared
- Journal of High Energy Physics, Vol. 2008, Issue 03
Cuba—a library for multidimensional numerical integration
journal, June 2007
- Hahn, Thomas
- Computer Physics Communications, Vol. 176, Issue 11-12
Distribution function approach to redshift space distortions. Part II:N-body simulations
text, January 2012
- Okumura, Teppei; Seljak, Uroš; McDonald, Patrick
- IOP Publishing
On the non-linear scale of cosmological perturbation theory
text, January 2013
- Blas, Diego; Garny, Mathias; Konstandin, Thomas
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Generation of Vorticity and Velocity Dispersion by Orbit Crossing
text, January 2008
- Pueblas, Sebastian; Scoccimarro, Roman
- arXiv
Contributions to the Dark Matter 3-Pt Function from the Radiation Era
text, January 2009
- Fitzpatrick, A. Liam; Senatore, Leonardo; Zaldarriaga, Matias
- arXiv
A critical look at cosmological perturbation theory techniques
text, January 2009
- Carlson, Jordan; White, Martin; Padmanabhan, Nikhil
- arXiv
Non-Gaussianities in Single Field Inflation and their Optimal Limits from the WMAP 5-year Data
text, January 2009
- Senatore, Leonardo; Smith, Kendrick M.; Zaldarriaga, Matias
- arXiv
Cosmological Non-Linearities as an Effective Fluid
text, January 2010
- Baumann, Daniel; Nicolis, Alberto; Senatore, Leonardo
- arXiv
Distribution function approach to redshift space distortions. Part II: N-body simulations
text, January 2011
- Okumura, Teppei; Seljak, Uros; McDonald, Patrick
- arXiv
Nonlinear Power Spectrum from Resummed Perturbation Theory: a Leap Beyond the BAO Scale
text, January 2012
- Anselmi, Stefano; Pietroni, Massimo
- arXiv
The Effective Field Theory of Cosmological Large Scale Structures
text, January 2012
- Carrasco, John Joseph M.; Hertzberg, Mark P.; Senatore, Leonardo
- arXiv
Symmetries and Consistency Relations in the Large Scale Structure of the Universe
text, January 2013
- Kehagias, A.; Riotto, A.
- arXiv
Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure
text, January 2013
- Peloso, Marco; Pietroni, Massimo
- arXiv
Large-Scale Structure of the Universe and Cosmological Perturbation Theory
text, January 2001
- Bernardeau, F.; Colombi, S.; Gaztanaga, E.
- arXiv
Loop Corrections in Non-Linear Cosmological Perturbation Theory
text, January 1995
- Scoccimarro, Roman; Frieman, Joshua
- arXiv
Works referencing / citing this record:
Cosmic Structure Formation with Kinetic Field Theory
journal, September 2019
- Bartelmann, Matthias; Kozlikin, Elena; Lilow, Robert
- Annalen der Physik, Vol. 531, Issue 11
Structure formation with massive neutrinos: going beyond linear theory
journal, November 2014
- Blas, Diego; Garny, Mathias; Konstandin, Thomas
- Journal of Cosmology and Astroparticle Physics, Vol. 2014, Issue 11
The IR-resummed Effective Field Theory of Large Scale Structures
journal, February 2015
- Senatore, Leonardo; Zaldarriaga, Matias
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 02
The bispectrum in the Effective Field Theory of Large Scale Structure
journal, May 2015
- Baldauf, Tobias; Mercolli, Lorenzo; Mirbabayi, Mehrdad
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 05
Analytic prediction of baryonic effects from the EFT of large scale structures
journal, May 2015
- Lewandowski, Matthew; Perko, Ashley; Senatore, Leonardo
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 05
The one-loop matter bispectrum in the Effective Field Theory of Large Scale Structures
journal, October 2015
- Angulo, Raul E.; Foreman, Simon; Schmittfull, Marcel
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 10
Bias in the effective field theory of large scale structures
journal, November 2015
- Senatore, Leonardo
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 11
Effective theory of large-scale structure with primordial non-Gaussianity
journal, November 2015
- Assassi, Valentin; Baumann, Daniel; Pajer, Enrico
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 11
Cosmological perturbation theory in 1+1 dimensions
journal, January 2016
- McQuinn, Matthew; White, Martin
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 01
On the reach of perturbative descriptions for dark matter displacement fields
journal, March 2016
- Baldauf, Tobias; Schaan, Emmanuel; Zaldarriaga, Matias
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 03
Perturbation theory, effective field theory, and oscillations in the power spectrum
journal, March 2016
- Vlah, Zvonimir; Seljak, Uroš; Chu, Man Yat
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 03
Precision comparison of the power spectrum in the EFTofLSS with simulations
journal, May 2016
- Foreman, Simon; Perrier, Hideki; Senatore, Leonardo
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 05
The trispectrum in the Effective Field Theory of Large Scale Structure
journal, June 2016
- Bertolini, Daniele; Schutz, Katelin; Solon, Mikhail P.
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 06
An extended action for the effective field theory of dark energy: a stability analysis and a complete guide to the mapping at the basis of EFTCAMB
journal, July 2016
- Frusciante, Noemi; Papadomanolakis, Georgios; Silvestri, Alessandra
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 07
Principal shapes and squeezed limits in the effective field theory of large scale structure
journal, November 2016
- Bertolini, Daniele; Solon, Mikhail P.
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 11
On the stability conditions for theories of modified gravity in the presence of matter fields
journal, March 2017
- De Felice, Antonio; Frusciante, Noemi; Papadomanolakis, Georgios
- Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 03
Efficient exploration of cosmology dependence in the EFT of LSS
journal, April 2017
- Cataneo, Matteo; Foreman, Simon; Senatore, Leonardo
- Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 04
The matter power spectrum in redshift space using effective field theory
journal, November 2017
- Bella, Lucía Fonseca de la; Regan, Donough; Seery, David
- Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 11
Dark energy and modified gravity in the Effective Field Theory of Large-Scale Structure
journal, April 2018
- Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo
- Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 04
Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals
journal, April 2018
- Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias
- Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 04
The generation of vorticity in cosmological N-body simulations
journal, September 2018
- Jelic-Cizmek, Goran; Lepori, Francesca; Adamek, Julian
- Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 09
The effective field theory of large scale structure at three loops
journal, November 2019
- Konstandin, Thomas; Porto, Rafael A.; Rubira, Henrique
- Journal of Cosmology and Astroparticle Physics, Vol. 2019, Issue 11
The properties of cosmic velocity fields
journal, October 2015
- Hahn, Oliver; Angulo, Raul E.; Abel, Tom
- Monthly Notices of the Royal Astronomical Society, Vol. 454, Issue 4
Matter bispectrum of large-scale structure: Three-dimensional comparison between theoretical models and numerical simulations
journal, April 2016
- Lazanu, Andrei; Giannantonio, Tommaso; Schmittfull, Marcel
- Physical Review D, Vol. 93, Issue 8
Non-Gaussian covariance of the matter power spectrum in the effective field theory of large scale structure
journal, June 2016
- Bertolini, Daniele; Schutz, Katelin; Solon, Mikhail P.
- Physical Review D, Vol. 93, Issue 12
Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals
journal, November 2016
- Schmittfull, Marcel; Vlah, Zvonimir
- Physical Review D, Vol. 94, Issue 10
EFT of large scale structures in redshift space
journal, March 2018
- Lewandowski, Matthew; Senatore, Leonardo; Prada, Francisco
- Physical Review D, Vol. 97, Issue 6
On the soft limit of the large scale structure power spectrum: UV dependence
text, January 2015
- Garny, Mathias; Konstandin, Thomas; Porto, Rafael A.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The Hunt for Primordial Interactions in the Large-Scale Structures of the Universe
journal, August 2019
- Biagetti, Matteo
- Galaxies, Vol. 7, Issue 3
On the soft limit of the large scale structure power spectrum: UV dependence
journal, November 2015
- Garny, Mathias; Konstandin, Thomas; Porto, Rafael A.
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 11
The effective field theory of large scale structure at three loops
text, January 2019
- Konstandin, Thomas; Porto, Rafael A.; Rubira, Henrique
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The Effective Field Theory of Large Scale Structure at Three Loops
text, January 2019
- Konstandin, Thomas; Porto, Rafael A.; Rubira, Henrique
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
The Properties of Cosmic Velocity Fields
text, January 2014
- Hahn, Oliver; Angulo, Raul E.; Abel, Tom
- arXiv
The IR-resummed Effective Field Theory of Large Scale Structures
text, January 2014
- Senatore, Leonardo; Zaldarriaga, Matias
- arXiv
The One-Loop Matter Bispectrum in the Effective Field Theory of Large Scale Structures
text, January 2014
- Angulo, Raul E.; Foreman, Simon; Schmittfull, Marcel
- arXiv
Lagrangian perturbation theory at one loop order: successes, failures, and improvements
text, January 2014
- Vlah, Zvonimir; Seljak, Uroš; Baldauf, Tobias
- arXiv
The Effective Field Theory of Large Scale Structure at Two Loops: the apparent scale dependence of the speed of sound
text, January 2015
- Baldauf, Tobias; Mercolli, Lorenzo; Zaldarriaga, Matias
- arXiv
Precision Comparison of the Power Spectrum in the EFTofLSS with Simulations
text, January 2015
- Foreman, Simon; Perrier, Hideki; Senatore, Leonardo
- arXiv
Perturbation theory, effective field theory, and oscillations in the power spectrum
text, January 2015
- Vlah, Zvonimir; Seljak, Uroš; Chu, Man Yat
- arXiv
An Extended action for the effective field theory of dark energy: a stability analysis and a complete guide to the mapping at the basis of EFTCAMB
text, January 2016
- Frusciante, Noemi; Papadomanolakis, Georgios; Silvestri, Alessandra
- arXiv
Principal Shapes and Squeezed Limits in the Effective Field Theory of Large Scale Structure
text, January 2016
- Bertolini, Daniele; Solon, Mikhail P.
- arXiv
FFT-PT: Reducing the two-loop large-scale structure power spectrum to low-dimensional radial integrals
text, January 2016
- Schmittfull, Marcel; Vlah, Zvonimir
- arXiv
On the stability conditions for theories of modified gravity in presence of matter fields
text, January 2016
- De Felice, Antonio; Frusciante, Noemi; Papadomanolakis, Georgios
- arXiv
The matter power spectrum in redshift space using effective field theory
text, January 2017
- de la Bella, Lucía Fonseca; Regan, Donough; Seery, David
- arXiv
Cosmological Perturbation Theory Using the FFTLog: Formalism and Connection to QFT Loop Integrals
text, January 2017
- Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias
- arXiv
Dark Energy and Modified Gravity in the Effective Field Theory of Large-Scale Structure
text, January 2017
- Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo
- arXiv
The Generation of Vorticity in Cosmological N-body Simulations
text, January 2018
- Jelic-Cizmek, Goran; Lepori, Francesca; Adamek, Julian
- arXiv
Cosmic Structure Formation with Kinetic Field Theory
text, January 2019
- Bartelmann, Matthias; Kozlikin, Elena; Lilow, Robert
- arXiv
The Effective Field Theory of Large Scale Structure at Three Loops
text, January 2019
- Konstandin, Thomas; Porto, Rafael A.; Rubira, Henrique
- arXiv