The Lagrangian-space Effective Field Theory of large scale structures

Porto, Rafael A.; Senatore, Leonardo; Zaldarriaga, Matias

doi:10.1088/1475-7516/2014/05/022

Title: The Lagrangian-space Effective Field Theory of large scale structures

Abstract

Here, we introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of extended objects in Lagrangian space. In LEFT the resulting finite size effects are described using a multipole expansion parameterized by a set of time dependent coefficients and organized in powers of the ratio of the wavenumber of interest k over the non-linear scale k_NL. The multipoles encode the effects of the short distance modes on the long-wavelength universe and absorb UV divergences when present. There are no IR divergences in LEFT. Some of the parameters that control the perturbative approach are not assumed to be small and can be automatically resummed. We present an illustrative one-loop calculation for a power law universe. We describe the dynamics both at the level of the equations of motion and through an action formalism.

Authors:

Porto, Rafael A. ^[1]; Senatore, Leonardo ^[2]; Zaldarriaga, Matias ^[3]

Institute for Advanced Study, Princeton, NJ (United States); Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States); European Organization for Nuclear Research (CERN), Geneva (Switzerland)
Institute for Advanced Study, Princeton, NJ (United States)

Publication Date:: Mon May 19 00:00:00 EDT 2014

Research Org.:: Stanford Univ., CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1491162

Grant/Contract Number:: SC0008078

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Cosmology and Astroparticle Physics

Additional Journal Information:: Journal Volume: 2014; Journal Issue: 05; Journal ID: ISSN 1475-7516

Publisher:: Institute of Physics (IOP)

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; dark matter theory; particle physics - cosmology connection; baryon acoustic oscillations; cosmological perturbation theory

Citation Formats


                    Porto, Rafael A., Senatore, Leonardo, and Zaldarriaga, Matias. The Lagrangian-space Effective Field Theory of large scale structures.  United States: N. p., 2014. 
Web.  doi:10.1088/1475-7516/2014/05/022.

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                    Porto, Rafael A., Senatore, Leonardo, & Zaldarriaga, Matias. The Lagrangian-space Effective Field Theory of large scale structures.  United States.  https://doi.org/10.1088/1475-7516/2014/05/022

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                    Porto, Rafael A., Senatore, Leonardo, and Zaldarriaga, Matias. Mon .  
"The Lagrangian-space Effective Field Theory of large scale structures".  United States.  https://doi.org/10.1088/1475-7516/2014/05/022.  https://www.osti.gov/servlets/purl/1491162.

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@article{osti_1491162,

  title        = {The Lagrangian-space Effective Field Theory of large scale structures},

  author       = {Porto, Rafael A. and Senatore, Leonardo and Zaldarriaga, Matias},

  abstractNote = {Here, we introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of extended objects in Lagrangian space. In LEFT the resulting finite size effects are described using a multipole expansion parameterized by a set of time dependent coefficients and organized in powers of the ratio of the wavenumber of interest k over the non-linear scale kNL. The multipoles encode the effects of the short distance modes on the long-wavelength universe and absorb UV divergences when present. There are no IR divergences in LEFT. Some of the parameters that control the perturbative approach are not assumed to be small and can be automatically resummed. We present an illustrative one-loop calculation for a power law universe. We describe the dynamics both at the level of the equations of motion and through an action formalism.},

  doi          = {10.1088/1475-7516/2014/05/022},

  journal      = {Journal of Cosmology and Astroparticle Physics},

  number       = 05,

  volume       = 2014,

  place        = {United States},

  year         = {Mon May 19 00:00:00 EDT 2014},

  month        = {Mon May 19 00:00:00 EDT 2014}

}

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https://doi.org/10.1088/1475-7516/2014/05/022

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Cited by: 132 works

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Figures / Tables:

Figure 1: Parameters measuring the amplitude of non-linear correction on a mode of wavenumber k. They quantify the motions created by modes longer (ϵ$_{\delta<}$) and shorter (ϵ$_{\delta<}$) than k and the tides from larger scales (ϵ$_{\delta<}$).

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The Lagrangian-space Effective Field Theory of large scale structures

Journal Article Porto, Rafael A. ; Zaldarriaga, Matias ; Senatore, Leonardo - Journal of Cosmology and Astroparticle Physics

We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of extended objects in Lagrangian space. In LEFT the resulting finite size effects are described using a multipole expansion parameterized by a set of time dependent coefficients and organized in powers of the ratio of the wavenumber of interest k over the non-linear scale k{sub NL}. The multipoles encode the effects of the short distance modes on the long-wavelength universe and absorb UV divergences when present. There are nomore »« less
https://doi.org/10.1088/1475-7516/2014/05/022
Bias in the effective field theory of large scale structures

Journal Article Senatore, Leonardo - Journal of Cosmology and Astroparticle Physics

We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what was recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local inmore »« less
https://doi.org/10.1088/1475-7516/2015/11/007
Bias in the effective field theory of large scale structures

Journal Article Senatore, Leonardo - Journal of Cosmology and Astroparticle Physics

We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what was recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local inmore »« less
Cited by 118
https://doi.org/10.1088/1475-7516/2015/11/007

Full Text Available
Resumming cosmological perturbations via the Lagrangian picture: One-loop results in real space and in redshift space

Journal Article Matsubara, Takahiko - Physical Review. D, Particles Fields

We develop a new approach to study the nonlinear evolution in the large-scale structure of the Universe both in real space and in redshift space, extending the standard perturbation theory of gravitational instability. Infinite series of terms in standard Eulerian perturbation theory are resummed as a result of our starting from a Lagrangian description of perturbations. Delicate nonlinear effects on scales of the baryon acoustic oscillations are more accurately described by our method than the standard one. Our approach differs from other resummation techniques recently proposed, such as the renormalized perturbation theory, etc., in that we use simple techniques andmore »« less
https://doi.org/10.1103/PHYSREVD.77.063530
Perturbation theory approach for the power spectrum: from dark matter in real space to massive haloes in redshift space

Journal Article Gil-Marín, Héctor ; Wagner, Christian ; Verde, Licia ; ... - Journal of Cosmology and Astroparticle Physics

We investigate the accuracy of Eulerian perturbation theory for describing the matter and galaxy power spectra in real and redshift space in light of future observational probes for precision cosmology. Comparing the analytical results with a large suite of N-body simulations (160 independent boxes of 13.8 (Gpc/h){sup 3} volume each, which are publicly available), we find that re-summing terms in the standard perturbative approach predicts the real-space matter power spectrum with an accuracy of ∼<2% for k ≤ 0.20 h/Mpc at redshifts z∼<1.5. This is obtained following the widespread technique of writing the resummed propagator in terms of 1-loop contributions.more »« less
https://doi.org/10.1088/1475-7516/2012/11/029

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Title: The Lagrangian-space Effective Field Theory of large scale structures

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Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak journal, August 2007

Large-scale structure of the Universe and cosmological perturbation theory journal, September 2002

Loop Corrections in Nonlinear Cosmological Perturbation Theory. II. Two‐Point Statistics and Self‐Similarity journal, December 1996

Cosmological non-linearities as an effective fluid journal, July 2012

The effective field theory of cosmological large scale structures journal, September 2012

Adhesive gravitational clustering journal, July 2005

Generation of vorticity and velocity dispersion by orbit crossing journal, August 2009

Coarse-grained cosmological perturbation theory journal, January 2012

On the renormalization of the effective field theory of large scale structures journal, August 2013

Estimating CDM particle trajectories in the mildly non-linear regime of structure formation. Implications for the density field in real and redshift space journal, December 2012

The Quantum Theory of Fields book, May 2013

Accuracy of Lagrangian approximations in voids journal, September 1996

Erratum: Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture [Phys. Rev. D 78 , 083519 (2008)] journal, November 2008

Resumming cosmological perturbations via the Lagrangian picture: One-loop results in real space and in redshift space journal, March 2008

On the velocity in the Effective Field Theory of Large Scale Structures journal, March 2014

Shift of the baryon acoustic oscillation scale: A simple physical picture journal, May 2012

Single-field consistency relations of large scale structure journal, December 2013

Symmetries and consistency relations in the large scale structure of the universe journal, August 2013

Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure journal, May 2013

Single-field consistency relations of large scale structure part II: resummation and redshift space journal, February 2014

Effective field theory of gravity for extended objects journal, May 2006

Post-Newtonian corrections to the motion of spinning bodies in nonrelativistic general relativity journal, May 2006

Gravitational radiative corrections from effective field theory journal, June 2010

Dissipative effects in the worldline approach to black hole dynamics journal, May 2006

Absorption effects due to spin in the worldline approach to black hole dynamics journal, March 2008

On the non-linear scale of cosmological perturbation theory journal, September 2013

On loops in inflation journal, December 2010

Field Theory for Today: The Quantum Theory of Fields . Volume 1, Foundations. Steven Weinberg. Cambridge University Press, New York, 1995. xxvi, 609 pp. $49.95 or £35. journal, September 1995

The Quantum Theory of Fields journal, October 1964

On the non-linear scale of cosmological perturbation theory text, January 2013

Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space text, January 2007

Generation of Vorticity and Velocity Dispersion by Orbit Crossing text, January 2008

Gravitational radiative corrections from effective field theory 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

Symmetries and Consistency Relations in the Large Scale Structure of the Universe text, January 2013

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

Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak text, January 2006

Cosmic Structure Formation with Kinetic Field Theory journal, September 2019

The Supersymmetric Effective Field Theory of Inflation journal, March 2017

The cosmic microwave background: the history of its experimental investigation and its significance for cosmology journal, June 2015

Lagrangian or Eulerian; real or Fourier? Not all approaches to large-scale structure are created equal journal, June 2014

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

A Lagrangian effective field theory journal, September 2015

The one-loop matter bispectrum in the Effective Field Theory of Large Scale Structures journal, October 2015

Bias in the effective field theory of large scale structures journal, November 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

Perturbation theory, effective field theory, and oscillations in the power spectrum journal, March 2016

Precision comparison of the power spectrum in the EFTofLSS with simulations journal, May 2016

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

A marked correlation function for constraining modified gravity models journal, November 2016

The Gaussian streaming model and convolution Lagrangian effective field theory journal, December 2016

On the stability conditions for theories of modified gravity in the presence of matter fields journal, March 2017

Efficient exploration of cosmology dependence in the EFT of LSS journal, April 2017

Modeling CMB lensing cross correlations with CLEFT journal, August 2017

The matter power spectrum in redshift space using effective field theory journal, November 2017

Biased tracers of two fluids in the Lagrangian picture journal, June 2019

The reconstructed power spectrum in the Zeldovich approximation journal, September 2019

The effective field theory of large scale structure at three loops journal, November 2019

Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals journal, November 2016

Nonlinear reconstruction of redshift space distortions journal, February 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

Lagrangian or Eulerian; Real or Fourier? Not All Approaches to Large-Scale Structure Are Created Equal text, January 2013

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

Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak
journal, August 2007

Large-scale structure of the Universe and cosmological perturbation theory
journal, September 2002

Loop Corrections in Nonlinear Cosmological Perturbation Theory. II. Two‐Point Statistics and Self‐Similarity
journal, December 1996

Cosmological non-linearities as an effective fluid
journal, July 2012

The effective field theory of cosmological large scale structures
journal, September 2012

Adhesive gravitational clustering
journal, July 2005

Generation of vorticity and velocity dispersion by orbit crossing
journal, August 2009

Coarse-grained cosmological perturbation theory
journal, January 2012

On the renormalization of the effective field theory of large scale structures
journal, August 2013

Estimating CDM particle trajectories in the mildly non-linear regime of structure formation. Implications for the density field in real and redshift space
journal, December 2012

The Quantum Theory of Fields
book, May 2013

Accuracy of Lagrangian approximations in voids
journal, September 1996

Erratum: Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture [Phys. Rev. D 78 , 083519 (2008)]
journal, November 2008

Resumming cosmological perturbations via the Lagrangian picture: One-loop results in real space and in redshift space
journal, March 2008

On the velocity in the Effective Field Theory of Large Scale Structures
journal, March 2014

Shift of the baryon acoustic oscillation scale: A simple physical picture
journal, May 2012

Single-field consistency relations of large scale structure
journal, December 2013

Symmetries and consistency relations in the large scale structure of the universe
journal, August 2013

Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure
journal, May 2013

Single-field consistency relations of large scale structure part II: resummation and redshift space
journal, February 2014

Effective field theory of gravity for extended objects
journal, May 2006

Post-Newtonian corrections to the motion of spinning bodies in nonrelativistic general relativity
journal, May 2006

Gravitational radiative corrections from effective field theory
journal, June 2010

Dissipative effects in the worldline approach to black hole dynamics
journal, May 2006

Absorption effects due to spin in the worldline approach to black hole dynamics
journal, March 2008

On the non-linear scale of cosmological perturbation theory
journal, September 2013

On loops in inflation
journal, December 2010

Field Theory for Today: The Quantum Theory of Fields . Volume 1, Foundations. Steven Weinberg. Cambridge University Press, New York, 1995. xxvi, 609 pp. $49.95 or £35.
journal, September 1995

The Quantum Theory of Fields
journal, October 1964

On the non-linear scale of cosmological perturbation theory
text, January 2013

Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
text, January 2007

Generation of Vorticity and Velocity Dispersion by Orbit Crossing
text, January 2008

Gravitational radiative corrections from effective field theory
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

Symmetries and Consistency Relations in the Large Scale Structure of the Universe
text, January 2013

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

Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak
text, January 2006

Cosmic Structure Formation with Kinetic Field Theory
journal, September 2019

The Supersymmetric Effective Field Theory of Inflation
journal, March 2017

The cosmic microwave background: the history of its experimental investigation and its significance for cosmology
journal, June 2015

Lagrangian or Eulerian; real or Fourier? Not all approaches to large-scale structure are created equal
journal, June 2014

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

A Lagrangian effective field theory
journal, September 2015

The one-loop matter bispectrum in the Effective Field Theory of Large Scale Structures
journal, October 2015

Bias in the effective field theory of large scale structures
journal, November 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

Perturbation theory, effective field theory, and oscillations in the power spectrum
journal, March 2016

Precision comparison of the power spectrum in the EFTofLSS with simulations
journal, May 2016

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

A marked correlation function for constraining modified gravity models
journal, November 2016

The Gaussian streaming model and convolution Lagrangian effective field theory
journal, December 2016

On the stability conditions for theories of modified gravity in the presence of matter fields
journal, March 2017

Efficient exploration of cosmology dependence in the EFT of LSS
journal, April 2017

Modeling CMB lensing cross correlations with CLEFT
journal, August 2017

The matter power spectrum in redshift space using effective field theory
journal, November 2017

Biased tracers of two fluids in the Lagrangian picture
journal, June 2019

The reconstructed power spectrum in the Zeldovich approximation
journal, September 2019

The effective field theory of large scale structure at three loops
journal, November 2019

Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals
journal, November 2016

Nonlinear reconstruction of redshift space distortions
journal, February 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

Lagrangian or Eulerian; Real or Fourier? Not All Approaches to Large-Scale Structure Are Created Equal
text, January 2013

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

Recursive Solutions of Lagrangian Perturbation Theory
text, January 2015

The Cosmic Microwave Background: The history of its experimental investigation and its significance for cosmology
text, January 2015

A Lagrangian effective field theory
text, January 2015

The Effective Field Theory of Large Scale Structure at Two Loops: the apparent scale dependence of the speed of sound
text, January 2015