Tensions between direct measurements of the lens power spectrum from Planck data

doi:10.1103/PhysRevD.97.103536

Title: Tensions between direct measurements of the lens power spectrum from Planck data

Abstract

We apply a recently developed method to directly measure the gravitational lensing power spectrum from CMB power spectra to the Planck satellite data. This method allows us to analyze the tension between the temperature power spectrum and lens reconstruction in a model independent way. Even when allowing for arbitrary variations in the lensing power spectrum, the tension remains at the 2.4σ level. By separating the lensing and unlensed high redshift information in the CMB power spectra, we also show that under ΛCDM the two are in tension at a similar level whereas the unlensed information is consistent with lensing reconstruction. These anomalies are driven by the smoother acoustic peaks relative to ΛCDM at ℓ ~1250-1500. Both tensions relax slightly when polarization data are considered. This technique also isolates the one combination of the lensing power spectrum multipoles that the Planck CMB power spectra currently constrain and can be straightforwardly generalized to future data when CMB power spectra constrain multiple aspects of lensing which are themselves correlated with lensing reconstruction

Authors:

Motloch, Pavel ^[1]; Hu, Wayne ^[1]

Univ. of Chicago, IL (United States). Kavli Inst. for Cosmological Physics (KICP)

Publication Date:: 2018-04-30

Research Org.:: Univ. of Chicago, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); National Aeronautic and Space Administration (NASA); National Science Foundation (NSF)

OSTI Identifier:: 1594000

Alternate Identifier(s):: OSTI ID: 1439499

Grant/Contract Number:: SC0009924; PHY-1125897; FG02-13ER41958

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 97; Journal Issue: 10; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS

Citation Formats


                    Motloch, Pavel, and Hu, Wayne. Tensions between direct measurements of the lens power spectrum from Planck data.  United States: N. p., 2018. 
        Web.  doi:10.1103/PhysRevD.97.103536.

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                    Motloch, Pavel, & Hu, Wayne. Tensions between direct measurements of the lens power spectrum from Planck data.  United States.  doi:10.1103/PhysRevD.97.103536.

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                    Motloch, Pavel, and Hu, Wayne. Mon .  
        "Tensions between direct measurements of the lens power spectrum from Planck data".  United States.  doi:10.1103/PhysRevD.97.103536.  https://www.osti.gov/servlets/purl/1594000.

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@article{osti_1594000,

  title        = {Tensions between direct measurements of the lens power spectrum from Planck data},

  author       = {Motloch, Pavel and Hu, Wayne},

  abstractNote = {We apply a recently developed method to directly measure the gravitational lensing power spectrum from CMB power spectra to the Planck satellite data. This method allows us to analyze the tension between the temperature power spectrum and lens reconstruction in a model independent way. Even when allowing for arbitrary variations in the lensing power spectrum, the tension remains at the 2.4σ level. By separating the lensing and unlensed high redshift information in the CMB power spectra, we also show that under ΛCDM the two are in tension at a similar level whereas the unlensed information is consistent with lensing reconstruction. These anomalies are driven by the smoother acoustic peaks relative to ΛCDM at ℓ ~1250-1500. Both tensions relax slightly when polarization data are considered. This technique also isolates the one combination of the lensing power spectrum multipoles that the Planck CMB power spectra currently constrain and can be straightforwardly generalized to future data when CMB power spectra constrain multiple aspects of lensing which are themselves correlated with lensing reconstruction},

  doi          = {10.1103/PhysRevD.97.103536},

  journal      = {Physical Review D},

  number       = 10,

  volume       = 97,

  place        = {United States},

  year         = {2018},

  month        = {4}

}

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DOI: 10.1103/PhysRevD.97.103536

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Works referenced in this record:

Reconstruction of lensing from the cosmic microwave background polarization
journal, October 2003

Hirata, Christopher M.; Seljak, Uroš
Physical Review D, Vol. 68, Issue 8
DOI: 10.1103/PhysRevD.68.083002

Two-season Atacama Cosmology Telescope polarimeter lensing power spectrum
journal, June 2017

Sherwin, Blake D.; van Engelen, Alexander; Sehgal, Neelima
Physical Review D, Vol. 95, Issue 12
DOI: 10.1103/PhysRevD.95.123529

Non-Gaussian structure of the lensed CMB power spectra covariance matrix
journal, December 2012

Benoit-Lévy, Aurélien; Smith, Kendrick M.; Hu, Wayne
Physical Review D, Vol. 86, Issue 12
DOI: 10.1103/PhysRevD.86.123008

Mass Reconstruction with Cosmic Microwave Background Polarization
journal, August 2002

Hu, Wayne; Okamoto, Takemi
The Astrophysical Journal, Vol. 574, Issue 2
DOI: 10.1086/341110

Inflationary features and shifts in cosmological parameters from Planck 2015 data
journal, October 2017

Obied, Georges; Dvorkin, Cora; Heinrich, Chen
Physical Review D, Vol. 96, Issue 8
DOI: 10.1103/PhysRevD.96.083526

A Measurement of the Damping tail of the Cosmic Microwave Background Power Spectrum with the South pole Telescope
journal, November 2011

Keisler, R.; Reichardt, C. L.; Aird, K. A.
The Astrophysical Journal, Vol. 743, Issue 1
DOI: 10.1088/0004-637X/743/1/28

Gravitational Lensing Effect on Cosmic Microwave Background Anisotropies: A Power Spectrum Approach
journal, May 1996

Seljak, Uros
The Astrophysical Journal, Vol. 463
DOI: 10.1086/177218

Inference from Iterative Simulation Using Multiple Sequences
journal, November 1992

Gelman, Andrew; Rubin, Donald B.
Statistical Science, Vol. 7, Issue 4
DOI: 10.1214/ss/1177011136

Lensing of the CMB: Non-Gaussian aspects
journal, August 2000

Zaldarriaga, Matias
Physical Review D, Vol. 62, Issue 6
DOI: 10.1103/PhysRevD.62.063510

MEASUREMENTS OF SUB-DEGREE B -MODE POLARIZATION IN THE COSMIC MICROWAVE BACKGROUND FROM 100 SQUARE DEGREES OF SPTPOL DATA
journal, July 2015

Keisler, R.; Hoover, S.; Harrington, N.
The Astrophysical Journal, Vol. 807, Issue 2
DOI: 10.1088/0004-637X/807/2/151

Angular trispectrum of the cosmic microwave background
journal, September 2001

Hu, Wayne
Physical Review D, Vol. 64, Issue 8
DOI: 10.1103/PhysRevD.64.083005

Weak gravitational lensing of the CMB
journal, June 2006

Lewis, A.; Challinor, A.
Physics Reports, Vol. 429, Issue 1
DOI: 10.1016/j.physrep.2006.03.002

Cosmic microwave background lensing reconstruction on the full sky
journal, April 2003

Okamoto, Takemi; Hu, Wayne
Physical Review D, Vol. 67, Issue 8
DOI: 10.1103/PhysRevD.67.083002

Cosmological parameters from CMB and other data: A Monte Carlo approach
journal, November 2002

Lewis, Antony; Bridle, Sarah
Physical Review D, Vol. 66, Issue 10
DOI: 10.1103/PhysRevD.66.103511

Cosmological information from lensed CMB power spectra
journal, December 2006

Smith, Kendrick M.; Hu, Wayne; Kaplinghat, Manoj
Physical Review D, Vol. 74, Issue 12
DOI: 10.1103/PhysRevD.74.123002

Planck 2015 results : XV. Gravitational lensing
journal, September 2016

Ade, P. A. R.; Aghanim, N.; Arnaud, M.
Astronomy & Astrophysics, Vol. 594
DOI: 10.1051/0004-6361/201525941

New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope : Implications for the Hubble Constant
journal, March 2018

Riess, Adam G.; Casertano, Stefano; Yuan, Wenlong
The Astrophysical Journal, Vol. 855, Issue 2
DOI: 10.3847/1538-4357/aaadb7

Complete reionization constraints from Planck 2015 polarization
journal, January 2017

Heinrich, Chen He; Miranda, Vinicius; Hu, Wayne
Physical Review D, Vol. 95, Issue 2
DOI: 10.1103/PhysRevD.95.023513

Correlation of CMB with large-scale structure. II. Weak lensing
journal, August 2008

Hirata, Christopher M.; Ho, Shirley; Padmanabhan, Nikhil
Physical Review D, Vol. 78, Issue 4
DOI: 10.1103/PhysRevD.78.043520

Delensing CMB polarization with external datasets
journal, June 2012

Smith, Kendrick M.; Hanson, Duncan; LoVerde, Marilena
Journal of Cosmology and Astroparticle Physics, Vol. 2012, Issue 06
DOI: 10.1088/1475-7516/2012/06/014

Internal delensing of Planck CMB temperature and polarization
journal, May 2017

Carron, Julien; Lewis, Antony; Challinor, Anthony
Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 05
DOI: 10.1088/1475-7516/2017/05/035

QUANTIFYING DISCORDANCE IN THE 2015 PLANCK CMB SPECTRUM
journal, February 2016

Addison, G. E.; Huang, Y.; Watts, D. J.
The Astrophysical Journal, Vol. 818, Issue 2
DOI: 10.3847/0004-637X/818/2/132

Lens covariance effects on likelihood analyses of CMB power spectra
journal, November 2017

Motloch, Pavel; Hu, Wayne
Physical Review D, Vol. 96, Issue 10
DOI: 10.1103/PhysRevD.96.103517

Planck 2013 results. XVI. Cosmological parameters
journal, October 2014

Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.
Astronomy & Astrophysics, Vol. 571
DOI: 10.1051/0004-6361/201321591

On Information and Sufficiency
journal, March 1951

Kullback, S.; Leibler, R. A.
The Annals of Mathematical Statistics, Vol. 22, Issue 1
DOI: 10.1214/aoms/1177729694

Planck 2013 results. XVII. Gravitational lensing by large-scale structure
journal, October 2014

Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.
Astronomy & Astrophysics, Vol. 571
DOI: 10.1051/0004-6361/201321543

Planck 2015 results : XIII. Cosmological parameters
journal, September 2016

Ade, P. A. R.; Aghanim, N.; Arnaud, M.
Astronomy & Astrophysics, Vol. 594
DOI: 10.1051/0004-6361/201525830

CMB lens sample covariance and consistency relations
journal, February 2017

Motloch, Pavel; Hu, Wayne; Benoit-Lévy, Aurélien
Physical Review D, Vol. 95, Issue 4
DOI: 10.1103/PhysRevD.95.043518

Detection of $B$ -Mode Polarization in the Cosmic Microwave Background with Data from the South Pole Telescope
journal, September 2013

Hanson, D.; Hoover, S.; Crites, A.
Physical Review Letters, Vol. 111, Issue 14
DOI: 10.1103/PhysRevLett.111.141301

Bicep2/ KECK ARRAY VIII: MEASUREMENT OF GRAVITATIONAL LENSING FROM LARGE-SCALE B -MODE POLARIZATION
journal, December 2016

Ade, P. A. R.; Ahmed, Z.; Aikin, R. W.
The Astrophysical Journal, Vol. 833, Issue 2
DOI: 10.3847/1538-4357/833/2/228

Model-independent reionization observables in the CMB
journal, July 2003

Hu, Wayne; Holder, Gilbert P.
Physical Review D, Vol. 68, Issue 2
DOI: 10.1103/PhysRevD.68.023001

Detection of the Power Spectrum of Cosmic Microwave Background Lensing by the Atacama Cosmology Telescope
journal, July 2011

Das, Sudeep; Sherwin, Blake D.; Aguirre, Paula
Physical Review Letters, Vol. 107, Issue 2
DOI: 10.1103/PhysRevLett.107.021301

Planck intermediate results : XLVII.
journal, December 2016

Adam, R.; Aghanim, N.; Ashdown, M.
Astronomy & Astrophysics, Vol. 596
DOI: 10.1051/0004-6361/201628897

Detection of gravitational lensing in the cosmic microwave background
journal, August 2007

Smith, Kendrick M.; Zahn, Oliver; Doré, Olivier
Physical Review D, Vol. 76, Issue 4
DOI: 10.1103/PhysRevD.76.043510

Planck intermediate results : LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters
journal, November 2017

Aghanim, N.; Akrami, Y.; Ashdown, M.
Astronomy & Astrophysics, Vol. 607
DOI: 10.1051/0004-6361/201629504

Planck 2015 results : XI. CMB power spectra, likelihoods, and robustness of parameters
journal, September 2016

Aghanim, N.; Arnaud, M.; Ashdown, M.
Astronomy & Astrophysics, Vol. 594
DOI: 10.1051/0004-6361/201526926

Planck 2015 results : XXIII. The thermal Sunyaev-Zeldovich effect-cosmic infrared background correlation
journal, September 2016

Ade, P. A. R.; Aghanim, N.; Arnaud, M.
Astronomy & Astrophysics, Vol. 594
DOI: 10.1051/0004-6361/201527418

Works referencing / citing this record:

Cornering the $P l a n c k$ $A_{lens}$ tension with future CMB data
journal, June 2018

Renzi, Fabrizio; Di Valentino, Eleonora; Melchiorri, Alessandro
Physical Review D, Vol. 97, Issue 12
DOI: 10.1103/physrevd.97.123534

Lensing covariance on cut sky and $SPT − P l a n c k$ lensing tensions
journal, January 2019

Motloch, Pavel; Hu, Wayne
Physical Review D, Vol. 99, Issue 2
DOI: 10.1103/physrevd.99.023506

Testing general relativity in cosmology
journal, December 2018

Ishak, Mustapha
Living Reviews in Relativity, Vol. 22, Issue 1
DOI: 10.1007/s41114-018-0017-4

Planck evidence for a closed Universe and a possible crisis for cosmology
journal, November 2019

Di Valentino, Eleonora; Melchiorri, Alessandro; Silk, Joseph
Nature Astronomy, Vol. 4, Issue 2
DOI: 10.1038/s41550-019-0906-9

Concordance and discordance in cosmology
journal, February 2019

Raveri, Marco; Hu, Wayne
Physical Review D, Vol. 99, Issue 4
DOI: 10.1103/physrevd.99.043506

Phenomenology of modified gravity at recombination
journal, February 2019

Lin, Meng-Xiang; Raveri, Marco; Hu, Wayne
Physical Review D, Vol. 99, Issue 4
DOI: 10.1103/physrevd.99.043514

Accounting for Correlations When Fitting Extra Cosmological Parameters
journal, September 2019

Huang, Y.; Addison, G. E.; Bennett, C. L.
The Astrophysical Journal, Vol. 882, Issue 2
DOI: 10.3847/1538-4357/ab3654

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Title: Tensions between direct measurements of the lens power spectrum from Planck data

Abstract

Citation Formats

Reconstruction of lensing from the cosmic microwave background polarization journal, October 2003

Two-season Atacama Cosmology Telescope polarimeter lensing power spectrum journal, June 2017

Non-Gaussian structure of the lensed CMB power spectra covariance matrix journal, December 2012

Mass Reconstruction with Cosmic Microwave Background Polarization journal, August 2002

Inflationary features and shifts in cosmological parameters from Planck 2015 data journal, October 2017

A Measurement of the Damping tail of the Cosmic Microwave Background Power Spectrum with the South pole Telescope journal, November 2011

Gravitational Lensing Effect on Cosmic Microwave Background Anisotropies: A Power Spectrum Approach journal, May 1996

Inference from Iterative Simulation Using Multiple Sequences journal, November 1992

Lensing of the CMB: Non-Gaussian aspects journal, August 2000

MEASUREMENTS OF SUB-DEGREE B -MODE POLARIZATION IN THE COSMIC MICROWAVE BACKGROUND FROM 100 SQUARE DEGREES OF SPTPOL DATA journal, July 2015

Angular trispectrum of the cosmic microwave background journal, September 2001

Weak gravitational lensing of the CMB journal, June 2006

Cosmic microwave background lensing reconstruction on the full sky journal, April 2003

Cosmological parameters from CMB and other data: A Monte Carlo approach journal, November 2002

Cosmological information from lensed CMB power spectra journal, December 2006

Planck 2015 results : XV. Gravitational lensing journal, September 2016

New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope : Implications for the Hubble Constant journal, March 2018

Complete reionization constraints from Planck 2015 polarization journal, January 2017

Correlation of CMB with large-scale structure. II. Weak lensing journal, August 2008

Delensing CMB polarization with external datasets journal, June 2012

Internal delensing of Planck CMB temperature and polarization journal, May 2017

QUANTIFYING DISCORDANCE IN THE 2015 PLANCK CMB SPECTRUM journal, February 2016

Lens covariance effects on likelihood analyses of CMB power spectra journal, November 2017

Planck 2013 results. XVI. Cosmological parameters journal, October 2014

On Information and Sufficiency journal, March 1951

Planck 2013 results. XVII. Gravitational lensing by large-scale structure journal, October 2014

Planck 2015 results : XIII. Cosmological parameters journal, September 2016

CMB lens sample covariance and consistency relations journal, February 2017

Detection of B -Mode Polarization in the Cosmic Microwave Background with Data from the South Pole Telescope journal, September 2013

Bicep2/ KECK ARRAY VIII: MEASUREMENT OF GRAVITATIONAL LENSING FROM LARGE-SCALE B -MODE POLARIZATION journal, December 2016

Model-independent reionization observables in the CMB journal, July 2003

Detection of the Power Spectrum of Cosmic Microwave Background Lensing by the Atacama Cosmology Telescope journal, July 2011

Planck intermediate results : XLVII. journal, December 2016

Detection of gravitational lensing in the cosmic microwave background journal, August 2007

Planck intermediate results : LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters journal, November 2017

Planck 2015 results : XI. CMB power spectra, likelihoods, and robustness of parameters journal, September 2016

Planck 2015 results : XXIII. The thermal Sunyaev-Zeldovich effect-cosmic infrared background correlation journal, September 2016

Cornering the P l a n c k A lens tension with future CMB data journal, June 2018

Lensing covariance on cut sky and SPT − P l a n c k lensing tensions journal, January 2019

Testing general relativity in cosmology journal, December 2018

Planck evidence for a closed Universe and a possible crisis for cosmology journal, November 2019

Concordance and discordance in cosmology journal, February 2019

Phenomenology of modified gravity at recombination journal, February 2019

Accounting for Correlations When Fitting Extra Cosmological Parameters journal, September 2019

Reconstruction of lensing from the cosmic microwave background polarization
journal, October 2003

Two-season Atacama Cosmology Telescope polarimeter lensing power spectrum
journal, June 2017

Non-Gaussian structure of the lensed CMB power spectra covariance matrix
journal, December 2012

Mass Reconstruction with Cosmic Microwave Background Polarization
journal, August 2002

Inflationary features and shifts in cosmological parameters from Planck 2015 data
journal, October 2017

A Measurement of the Damping tail of the Cosmic Microwave Background Power Spectrum with the South pole Telescope
journal, November 2011

Gravitational Lensing Effect on Cosmic Microwave Background Anisotropies: A Power Spectrum Approach
journal, May 1996

Inference from Iterative Simulation Using Multiple Sequences
journal, November 1992

Lensing of the CMB: Non-Gaussian aspects
journal, August 2000

MEASUREMENTS OF SUB-DEGREE B -MODE POLARIZATION IN THE COSMIC MICROWAVE BACKGROUND FROM 100 SQUARE DEGREES OF SPTPOL DATA
journal, July 2015

Angular trispectrum of the cosmic microwave background
journal, September 2001

Weak gravitational lensing of the CMB
journal, June 2006

Cosmic microwave background lensing reconstruction on the full sky
journal, April 2003

Cosmological parameters from CMB and other data: A Monte Carlo approach
journal, November 2002

Cosmological information from lensed CMB power spectra
journal, December 2006

Planck 2015 results : XV. Gravitational lensing
journal, September 2016

New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope : Implications for the Hubble Constant
journal, March 2018

Complete reionization constraints from Planck 2015 polarization
journal, January 2017

Correlation of CMB with large-scale structure. II. Weak lensing
journal, August 2008

Delensing CMB polarization with external datasets
journal, June 2012

Internal delensing of Planck CMB temperature and polarization
journal, May 2017

QUANTIFYING DISCORDANCE IN THE 2015 PLANCK CMB SPECTRUM
journal, February 2016

Lens covariance effects on likelihood analyses of CMB power spectra
journal, November 2017

Planck 2013 results. XVI. Cosmological parameters
journal, October 2014

On Information and Sufficiency
journal, March 1951

Planck 2013 results. XVII. Gravitational lensing by large-scale structure
journal, October 2014

Planck 2015 results : XIII. Cosmological parameters
journal, September 2016

CMB lens sample covariance and consistency relations
journal, February 2017

Detection of $B$ -Mode Polarization in the Cosmic Microwave Background with Data from the South Pole Telescope
journal, September 2013

Bicep2/ KECK ARRAY VIII: MEASUREMENT OF GRAVITATIONAL LENSING FROM LARGE-SCALE B -MODE POLARIZATION
journal, December 2016

Model-independent reionization observables in the CMB
journal, July 2003

Detection of the Power Spectrum of Cosmic Microwave Background Lensing by the Atacama Cosmology Telescope
journal, July 2011

Planck intermediate results : XLVII.
journal, December 2016

Detection of gravitational lensing in the cosmic microwave background
journal, August 2007

Planck intermediate results : LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters
journal, November 2017

Planck 2015 results : XI. CMB power spectra, likelihoods, and robustness of parameters
journal, September 2016

Planck 2015 results : XXIII. The thermal Sunyaev-Zeldovich effect-cosmic infrared background correlation
journal, September 2016

Cornering the $P l a n c k$ $A_{lens}$ tension with future CMB data
journal, June 2018

Lensing covariance on cut sky and $SPT − P l a n c k$ lensing tensions
journal, January 2019

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journal, December 2018

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journal, November 2019

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journal, February 2019

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journal, February 2019

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