Testing general relativity on cosmological scales at redshift z ∼ 1.5 with quasar and CMB lensing
Abstract
ABSTRACT We test general relativity (GR) at the effective redshift $$\bar{z} \sim 1.5$$ by estimating the statistic EG, a probe of gravity, on cosmological scales $$19 - 190\, h^{-1}{\rm Mpc}$$. This is the highest redshift and largest scale estimation of EG so far. We use the quasar sample with redshifts 0.8 < z < 2.2 from Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 16 as the large-scale structure (LSS) tracer, for which the angular power spectrum $$C_\ell ^{qq}$$ and the redshift-space distortion parameter β are estimated. By cross-correlating with the Planck 2018 cosmic microwave background (CMB) lensing map, we detect the angular cross-power spectrum $$C_\ell ^{\kappa q}$$ signal at $$12\, \sigma$$ significance. Both jackknife resampling and simulations are used to estimate the covariance matrix (CM) of EG at five bins covering different scales, with the later preferred for its better constraints on the covariances. We find EG estimates agree with the GR prediction at $$1\, \sigma$$ level over all these scales. With the CM estimated with 300 simulations, we report a best-fitting scale-averaged estimate of $$E_G(\bar{z})=0.30\pm 0.05$$, which is in line with the GR prediction $$E_G^{\rm GR}(\bar{z})=0.33$$ with Planck 2018 CMB + BAO matter density fraction Ωm = 0.31. The statistical errors of EG with future LSS surveys at similar redshifts will be reduced by an order of magnitude, which makes it possible to constrain modified gravity models.
- Authors:
-
- Center for Cosmology and Particle Physics, Department of Physics, New York University, 726 Broadway, New York, NY 10003, USA
- Center for Cosmology and Particle Physics, Department of Physics, New York University, 726 Broadway, New York, NY 10003, USA, Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA
- Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
- Berkeley Center for Cosmological Physics, University of California, Berkeley, CA 94720, USA
- IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
- Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94305, USA
- Max–Planck–Institut für Extraterrestrische Physik, Postfach 1312, Giessenbachstrasse 1, D-85748 Garching bei München, Germany
- University of Wyoming, 1000 E. University Ave., Laramie, WY 82071, USA
- Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, OH, USA
- Department of Physics and Astronomy, Sejong University, Seoul 143-747, Korea
- Institute of Physics, Laboratory of Astrophysics, École Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, CH-1290 Versoix, Switzerland
- Publication Date:
- Research Org.:
- Univ. of Wyoming, Laramie, WY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Aeronautics and Space Administration (NASA); European Research Council (ERC); National Research Foundation of Korea (NRF)
- OSTI Identifier:
- 1745064
- Alternate Identifier(s):
- OSTI ID: 1787340
- Grant/Contract Number:
- SC0019022; 80NSSC18K1014; NNH17ZDA001N; 670193; 2017R1E1A1A01077508; 2020R1A2C1005655
- Resource Type:
- Published Article
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Additional Journal Information:
- Journal Name: Monthly Notices of the Royal Astronomical Society Journal Volume: 501 Journal Issue: 1; Journal ID: ISSN 0035-8711
- Publisher:
- Oxford University Press
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; cosmology: theory; cosmology: observations; large-scale structure of Universe; gravitation; gravitational lensing: weak; cosmic background radiation
Citation Formats
Zhang, Yucheng, Pullen, Anthony R., Alam, Shadab, Singh, Sukhdeep, Burtin, Etienne, Chuang, Chia-Hsun, Hou, Jiamin, Lyke, Brad W., Myers, Adam D., Neveux, Richard, Ross, Ashley J., Rossi, Graziano, and Zhao, Cheng. Testing general relativity on cosmological scales at redshift z ∼ 1.5 with quasar and CMB lensing. United Kingdom: N. p., 2020.
Web. doi:10.1093/mnras/staa3672.
Zhang, Yucheng, Pullen, Anthony R., Alam, Shadab, Singh, Sukhdeep, Burtin, Etienne, Chuang, Chia-Hsun, Hou, Jiamin, Lyke, Brad W., Myers, Adam D., Neveux, Richard, Ross, Ashley J., Rossi, Graziano, & Zhao, Cheng. Testing general relativity on cosmological scales at redshift z ∼ 1.5 with quasar and CMB lensing. United Kingdom. https://doi.org/10.1093/mnras/staa3672
Zhang, Yucheng, Pullen, Anthony R., Alam, Shadab, Singh, Sukhdeep, Burtin, Etienne, Chuang, Chia-Hsun, Hou, Jiamin, Lyke, Brad W., Myers, Adam D., Neveux, Richard, Ross, Ashley J., Rossi, Graziano, and Zhao, Cheng. Wed .
"Testing general relativity on cosmological scales at redshift z ∼ 1.5 with quasar and CMB lensing". United Kingdom. https://doi.org/10.1093/mnras/staa3672.
@article{osti_1745064,
title = {Testing general relativity on cosmological scales at redshift z ∼ 1.5 with quasar and CMB lensing},
author = {Zhang, Yucheng and Pullen, Anthony R. and Alam, Shadab and Singh, Sukhdeep and Burtin, Etienne and Chuang, Chia-Hsun and Hou, Jiamin and Lyke, Brad W. and Myers, Adam D. and Neveux, Richard and Ross, Ashley J. and Rossi, Graziano and Zhao, Cheng},
abstractNote = {ABSTRACT We test general relativity (GR) at the effective redshift $\bar{z} \sim 1.5$ by estimating the statistic EG, a probe of gravity, on cosmological scales $19 - 190\, h^{-1}{\rm Mpc}$. This is the highest redshift and largest scale estimation of EG so far. We use the quasar sample with redshifts 0.8 < z < 2.2 from Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 16 as the large-scale structure (LSS) tracer, for which the angular power spectrum $C_\ell ^{qq}$ and the redshift-space distortion parameter β are estimated. By cross-correlating with the Planck 2018 cosmic microwave background (CMB) lensing map, we detect the angular cross-power spectrum $C_\ell ^{\kappa q}$ signal at $12\, \sigma$ significance. Both jackknife resampling and simulations are used to estimate the covariance matrix (CM) of EG at five bins covering different scales, with the later preferred for its better constraints on the covariances. We find EG estimates agree with the GR prediction at $1\, \sigma$ level over all these scales. With the CM estimated with 300 simulations, we report a best-fitting scale-averaged estimate of $E_G(\bar{z})=0.30\pm 0.05$, which is in line with the GR prediction $E_G^{\rm GR}(\bar{z})=0.33$ with Planck 2018 CMB + BAO matter density fraction Ωm = 0.31. The statistical errors of EG with future LSS surveys at similar redshifts will be reduced by an order of magnitude, which makes it possible to constrain modified gravity models.},
doi = {10.1093/mnras/staa3672},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 1,
volume = 501,
place = {United Kingdom},
year = {2020},
month = {11}
}
https://doi.org/10.1093/mnras/staa3672
Works referenced in this record:
Confirmation of general relativity on large scales from weak lensing and galaxy velocities
journal, March 2010
- Reyes, Reinabelle; Mandelbaum, Rachel; Seljak, Uros
- Nature, Vol. 464, Issue 7286
Lensing corrections to the E g ( z ) statistics from large scale structure
journal, September 2016
- Dizgah, Azadeh Moradinezhad; Durrer, Ruth
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 09
RCSLenS: testing gravitational physics through the cross-correlation of weak lensing and large-scale structure
journal, December 2015
- Blake, Chris; Joudaki, Shahab; Heymans, Catherine
- Monthly Notices of the Royal Astronomical Society, Vol. 456, Issue 3
Microwave Background Radiation as a Probe of the Contemporary Structure and History of the Universe
journal, September 1980
- Sunyaev, R. A.; Zel'dovich, Ya. B.
- Annual Review of Astronomy and Astrophysics, Vol. 18, Issue 1
The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: N-body mock challenge for the quasar sample
journal, September 2020
- Smith, Alex; Burtin, Etienne; Hou, Jiamin
- Monthly Notices of the Royal Astronomical Society, Vol. 499, Issue 1
The Sdss-Iv Extended Baryon Oscillation Spectroscopic Survey: Overview and Early data
journal, February 2016
- Dawson, Kyle S.; Kneib, Jean-Paul; Percival, Will J.
- The Astronomical Journal, Vol. 151, Issue 2
CMB lensing tomography with the DES Science Verification galaxies
journal, January 2016
- Giannantonio, T.; Fosalba, P.; Cawthon, R.
- Monthly Notices of the Royal Astronomical Society, Vol. 456, Issue 3
Towards an accurate model of the redshift-space clustering of haloes in the quasi-linear regime: Redshift-space distortions
journal, August 2011
- Reid, Beth A.; White, Martin
- Monthly Notices of the Royal Astronomical Society, Vol. 417, Issue 3
The Sdss-Iv Extended Baryon Oscillation Spectroscopic Survey: Quasar Target Selection
journal, December 2015
- Myers, Adam D.; Palanque-Delabrouille, Nathalie; Prakash, Abhishek
- The Astrophysical Journal Supplement Series, Vol. 221, Issue 2
Maps of Dust Infrared Emission for Use in Estimation of Reddening and Cosmic Microwave Background Radiation Foregrounds
journal, June 1998
- Schlegel, David J.; Finkbeiner, Douglas P.; Davis, Marc
- The Astrophysical Journal, Vol. 500, Issue 2
Sloan Digital Sky Survey IV: Mapping the Milky Way, Nearby Galaxies, and the Distant Universe
journal, June 2017
- Blanton, Michael R.; Bershady, Matthew A.; Abolfathi, Bela
- The Astronomical Journal, Vol. 154, Issue 1
Large-scale bias and the peak background split
journal, September 1999
- Sheth, Ravi K.; Tormen, Giuseppe
- Monthly Notices of the Royal Astronomical Society, Vol. 308, Issue 1
The Zel'dovich approximation
journal, February 2014
- White, Martin
- Monthly Notices of the Royal Astronomical Society, Vol. 439, Issue 4
The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the quasar sample in configuration space between redshift 0.8 and 2.2
journal, October 2020
- Hou, Jiamin; Sánchez, Ariel G.; Ross, Ashley J.
- Monthly Notices of the Royal Astronomical Society, Vol. 500, Issue 1
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
The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from the anisotropic power spectrum of the quasar sample between redshift 0.8 and 2.2
journal, September 2020
- Neveux, Richard; Burtin, Etienne; de Mattia, Arnaud
- Monthly Notices of the Royal Astronomical Society, Vol. 499, Issue 1
Testing gravity using galaxy-galaxy lensing and clustering amplitudes in KiDS-1000, BOSS, and 2dFLenS
journal, October 2020
- Blake, Chris; Amon, Alexandra; Asgari, Marika
- Astronomy & Astrophysics, Vol. 642
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
The Simons Observatory: science goals and forecasts
journal, February 2019
- Ade, Peter; Aguirre, James; Ahmed, Zeeshan
- Journal of Cosmology and Astroparticle Physics, Vol. 2019, Issue 02
How to measure CMB power spectra without losing information
journal, May 1997
- Tegmark, Max
- Physical Review D, Vol. 55, Issue 10
The Power Spectrum of the CfA/SSRS UZC Galaxy Redshift Survey
journal, March 2001
- Padmanabhan, Nikhil; Tegmark, Max; Hamilton, Andrew J. S.
- The Astrophysical Journal, Vol. 550, Issue 1
theories of gravity
journal, March 2010
- Sotiriou, Thomas P.; Faraoni, Valerio
- Reviews of Modern Physics, Vol. 82, Issue 1
HEALPix: A Framework for High‐Resolution Discretization and Fast Analysis of Data Distributed on the Sphere
journal, April 2005
- Gorski, K. M.; Hivon, E.; Banday, A. J.
- The Astrophysical Journal, Vol. 622, Issue 2
The Multi-Object, Fiber-Fed Spectrographs for the Sloan Digital sky Survey and the Baryon Oscillation Spectroscopic Survey
journal, July 2013
- Smee, Stephen A.; Gunn, James E.; Uomoto, Alan
- The Astronomical Journal, Vol. 146, Issue 2
The clustering of luminous red galaxies in the Sloan Digital Sky Survey imaging data
journal, June 2007
- Padmanabhan, Nikhil; Schlegel, David J.; Seljak, Uroš
- Monthly Notices of the Royal Astronomical Society, Vol. 378, Issue 3
Testing gravity on large scales by combining weak lensing with galaxy clustering using CFHTLenS and BOSS CMASS
journal, November 2016
- Alam, Shadab; Miyatake, Hironao; More, Surhud
- Monthly Notices of the Royal Astronomical Society, Vol. 465, Issue 4
emcee : The MCMC Hammer
journal, March 2013
- Foreman-Mackey, Daniel; Hogg, David W.; Lang, Dustin
- Publications of the Astronomical Society of the Pacific, Vol. 125, Issue 925
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: on the measurement of growth rate using galaxy correlation functions
journal, April 2017
- Satpathy, Siddharth; Alam, Shadab; Ho, Shirley
- Monthly Notices of the Royal Astronomical Society, Vol. 469, Issue 2
Planck 2018 results: I. Overview and the cosmological legacy of Planck
journal, September 2020
- Aghanim, N.; Akrami, Y.; Arroja, F.
- Astronomy & Astrophysics, Vol. 641
The Sloan Digital Sky Survey Quasar Catalog: Sixteenth Data Release
journal, August 2020
- Lyke, Brad W.; Higley, Alexandra N.; McLane, J. N.
- The Astrophysical Journal Supplement Series, Vol. 250, Issue 1
The 16th Data Release of the Sloan Digital Sky Surveys: First Release from the APOGEE-2 Southern Survey and Full Release of eBOSS Spectra
journal, June 2020
- Ahumada, Romina; Prieto, Carlos Allende; Almeida, Andrés
- The Astrophysical Journal Supplement Series, Vol. 249, Issue 1
Correlation of CMB with large-scale structure. I. Integrated Sachs-Wolfe tomography and cosmological implications
journal, August 2008
- Ho, Shirley; Hirata, Christopher; Padmanabhan, Nikhil
- Physical Review D, Vol. 78, Issue 4
Imprints of primordial non-Gaussianities on large-scale structure: Scale-dependent bias and abundance of virialized objects
journal, June 2008
- Dalal, Neal; Doré, Olivier; Huterer, Dragan
- Physical Review D, Vol. 77, Issue 12
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
journal, March 2017
- Alam, Shadab; Ata, Metin; Bailey, Stephen
- Monthly Notices of the Royal Astronomical Society, Vol. 470, Issue 3
4D gravity on a brane in 5D Minkowski space
journal, July 2000
- Dvali, Gia; Gabadadze, Gregory; Porrati, Massimo
- Physics Letters B, Vol. 485, Issue 1-3
Power-spectrum analysis of three-dimensional redshift surveys
journal, May 1994
- Feldman, Hume A.; Kaiser, Nick; Peacock, John A.
- The Astrophysical Journal, Vol. 426
Anisotropic magnification distortion of the 3D galaxy correlation. I. Real space
journal, November 2007
- Hui, Lam; Gaztañaga, Enrique; LoVerde, Marilena
- Physical Review D, Vol. 76, Issue 10
Cross-correlation of CMB with large-scale structure: Weak gravitational lensing
journal, November 2004
- Hirata, Christopher M.; Padmanabhan, Nikhil; Seljak, Uroš
- Physical Review D, Vol. 70, Issue 10
The VIMOS Public Extragalactic Redshift Survey (VIPERS): Gravity test from the combination of redshift-space distortions and galaxy-galaxy lensing at 0.5 < z < 1.2⋆
journal, December 2017
- de la Torre, S.; Jullo, E.; Giocoli, C.
- Astronomy & Astrophysics, Vol. 608
Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
journal, September 1998
- Riess, Adam G.; Filippenko, Alexei V.; Challis, Peter
- The Astronomical Journal, Vol. 116, Issue 3
corrfunc – a suite of blazing fast correlation functions on the CPU
journal, November 2019
- Sinha, Manodeep; Garrison, Lehman H.
- Monthly Notices of the Royal Astronomical Society, Vol. 491, Issue 2
Modified gravity and cosmology
journal, March 2012
- Clifton, Timothy; Ferreira, Pedro G.; Padilla, Antonio
- Physics Reports, Vol. 513, Issue 1-3
The cosmological constant and dark energy
journal, April 2003
- Peebles, P. J. E.; Ratra, Bharat
- Reviews of Modern Physics, Vol. 75, Issue 2
Planck 2018 results: VIII. Gravitational lensing
journal, September 2020
- Aghanim, N.; Akrami, Y.; Ashdown, M.
- Astronomy & Astrophysics, Vol. 641
Approaches to understanding cosmic acceleration
journal, August 2009
- Silvestri, Alessandra; Trodden, Mark
- Reports on Progress in Physics, Vol. 72, Issue 9
Probing Gravity at Cosmological Scales by Measurements which Test the Relationship between Gravitational Lensing and Matter Overdensity
journal, October 2007
- Zhang, Pengjie; Liguori, Michele; Bean, Rachel
- Physical Review Letters, Vol. 99, Issue 14
A relation between distance and radial velocity among extra-galactic nebulae
journal, March 1929
- Hubble, E.
- Proceedings of the National Academy of Sciences, Vol. 15, Issue 3
An analytic model for redshift-space distortions
journal, November 2013
- Wang, Lile; Reid, Beth; White, Martin
- Monthly Notices of the Royal Astronomical Society, Vol. 437, Issue 1
Testing gravity with CAMB and CosmoMC
journal, August 2011
- Hojjati, Alireza; Pogosian, Levon; Zhao, Gong-Bo
- Journal of Cosmology and Astroparticle Physics, Vol. 2011, Issue 08
Probing gravity at large scales through CMB lensing
journal, April 2015
- Pullen, Anthony R.; Alam, Shadab; Ho, Shirley
- Monthly Notices of the Royal Astronomical Society, Vol. 449, Issue 4
Redshift-weighted constraints on primordial non-Gaussianity from the clustering of the eBOSS DR14 quasars in Fourier space
journal, September 2019
- Castorina, Emanuele; Hand, Nick; Seljak, Uroš
- Journal of Cosmology and Astroparticle Physics, Vol. 2019, Issue 09
Planck 2015 results : XXVI. The Second
journal, September 2016
- Ade, P. A. R.; Aghanim, N.; Argüeso, F.
- Astronomy & Astrophysics, Vol. 594
Planck 2015 results : XXVII. The second
journal, September 2016
- Ade, P. A. R.; Aghanim, N.; Arnaud, M.
- Astronomy & Astrophysics, Vol. 594
The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measurement of the growth rate of structure from the anisotropic correlation function between redshift 0.8 and 2.2
journal, February 2018
- Zarrouk, Pauline; Burtin, Etienne; Gil-Marín, Héctor
- Monthly Notices of the Royal Astronomical Society, Vol. 477, Issue 2
Calibrating magnification bias for the EG statistic to test general relativity
journal, September 2018
- Yang, S.; Pullen, Anthony R.
- Monthly Notices of the Royal Astronomical Society, Vol. 481, Issue 2
An evolution free test for non-zero cosmological constant
journal, October 1979
- Alcock, Charles; Paczyński, Bohdan
- Nature, Vol. 281, Issue 5730
Dark Energy Versus Modified Gravity
journal, October 2016
- Joyce, Austin; Lombriser, Lucas; Schmidt, Fabian
- Annual Review of Nuclear and Particle Science, Vol. 66, Issue 1
Impact of magnification and size bias on the weak lensing power spectrum and peak statistics
journal, January 2014
- Liu, Jia; Haiman, Zoltán; Hui, Lam
- Physical Review D, Vol. 89, Issue 2
Planck 2018 results: IX. Constraints on primordial non-Gaussianity
journal, September 2020
- Akrami, Y.; Arroja, F.; Ashdown, M.
- Astronomy & Astrophysics, Vol. 641
KiDS+2dFLenS+GAMA: testing the cosmological model with the EG statistic
journal, June 2018
- Amon, A.; Blake, C.; Heymans, C.
- Monthly Notices of the Royal Astronomical Society, Vol. 479, Issue 3
Planck 2018 results: VI. Cosmological parameters
journal, September 2020
- Aghanim, N.; Akrami, Y.; Ashdown, M.
- Astronomy & Astrophysics, Vol. 641, A6
Cosmology of generalized modified gravity models
journal, March 2005
- Carroll, Sean M.; De Felice, Antonio; Duvvuri, Vikram
- Physical Review D, Vol. 71, Issue 6
ChainConsumer
journal, August 2016
- Hinton, Samuel
- The Journal of Open Source Software, Vol. 1, Issue 4
Testing general relativity with growth rate measurement from Sloan Digital Sky Survey – III. Baryon Oscillations Spectroscopic Survey galaxies
journal, August 2015
- Alam, Shadab; Ho, Shirley; Vargas-Magaña, Mariana
- Monthly Notices of the Royal Astronomical Society, Vol. 453, Issue 2
Clustering of quasars in SDSS-IV eBOSS: study of potential systematics and bias determination
journal, July 2017
- Laurent, Pierre; Eftekharzadeh, Sarah; Goff, Jean-Marc Le
- Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 07
The clustering of Galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: including covariance matrix errors
journal, February 2014
- Percival, Will J.; Ross, Ashley J.; Sánchez, Ariel G.
- Monthly Notices of the Royal Astronomical Society, Vol. 439, Issue 3
Planck 2015 results : XXVIII. The
journal, September 2016
- Ade, P. A. R.; Aghanim, N.; Arnaud, M.
- Astronomy & Astrophysics, Vol. 594
Convolution Lagrangian perturbation theory for biased tracers
journal, December 2012
- Carlson, Jordan; Reid, Beth; White, Martin
- Monthly Notices of the Royal Astronomical Society, Vol. 429, Issue 2
Probing gravitational lensing of the CMB with SDSS-IV quasars
journal, February 2019
- Han, Jiashu; Ferraro, Simone; Giusarma, Elena
- Monthly Notices of the Royal Astronomical Society, Vol. 485, Issue 2
Bias and variance of angular correlation functions
journal, July 1993
- Landy, Stephen D.; Szalay, Alexander S.
- The Astrophysical Journal, Vol. 412
Probing gravity with a joint analysis of galaxy and CMB lensing and SDSS spectroscopy
journal, October 2018
- Singh, Sukhdeep; Alam, Shadab; Mandelbaum, Rachel
- Monthly Notices of the Royal Astronomical Society, Vol. 482, Issue 1
A unified pseudo- C ℓ framework
journal, January 2019
- Alonso, David; Sanchez, Javier; Slosar, Anže
- Monthly Notices of the Royal Astronomical Society, Vol. 484, Issue 3
Why your model parameter confidences might be too optimistic. Unbiased estimation of the inverse covariance matrix
journal, December 2006
- Hartlap, J.; Simon, P.; Schneider, P.
- Astronomy & Astrophysics, Vol. 464, Issue 1
Testing general relativity in cosmology
journal, December 2018
- Ishak, Mustapha
- Living Reviews in Relativity, Vol. 22, Issue 1
Measurements of Ω and Λ from 42 High‐Redshift Supernovae
journal, June 1999
- Perlmutter, S.; Aldering, G.; Goldhaber, G.
- The Astrophysical Journal, Vol. 517, Issue 2
Constraining gravity at the largest scales through CMB lensing and galaxy velocities
journal, May 2016
- Pullen, Anthony R.; Alam, Shadab; He, Siyu
- Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 4
EZmocks: extending the Zel'dovich approximation to generate mock galaxy catalogues with accurate clustering statistics
journal, November 2014
- Chuang, Chia-Hsun; Kitaura, Francisco-Shu; Prada, Francisco
- Monthly Notices of the Royal Astronomical Society, Vol. 446, Issue 3
The 2.5 m Telescope of the Sloan Digital Sky Survey
journal, April 2006
- Gunn, James E.; Siegmund, Walter A.; Mannery, Edward J.
- The Astronomical Journal, Vol. 131, Issue 4
The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale structure catalogues for cosmological analysis
journal, September 2020
- Ross, Ashley J.; Bautista, Julian; Tojeiro, Rita
- Monthly Notices of the Royal Astronomical Society, Vol. 498, Issue 2
Putting the precision in precision cosmology: How accurate should your data covariance matrix be?
journal, May 2013
- Taylor, A.; Joachimi, B.; Kitching, T.
- Monthly Notices of the Royal Astronomical Society, Vol. 432, Issue 3