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Euclid: Covariance of weak lensing pseudo-C_ℓ estimates. Calculation, comparison to simulations, and dependence on survey geometry

Upham, R. E. and Brown, M. L. and Whittaker, L. and Amara, A. and Auricchio, N. and Bonino, D. and Branchini, E. and Brescia, M. and Brinchmann, J. and Capobianco, V. and Carbone, C. and Carretero, J. and Castellano, M. and Cavuoti, S. and Cimatti, A. and Cledassou, R. and Congedo, G. and Conversi, L. and Copin, Y. and Corcione, L. and Cropper, M. and Da Silva, A. and Degaudenzi, H. and Douspis, M. and Dubath, F. and Duncan, C. A. J. and Dupac, X. and Dusini, S. and Ealet, A. and Farrens, S. and Ferriol, S. and Fosalba, P. and Frailis, M. and Franceschi, E. and Fumana, M. and Garilli, B. and Gillis, B. and Giocoli, C. and Grupp, F. and Haugan, S. V. H. and Hoekstra, H. and Holmes, W. and Hormuth, F. and Hornstrup, A. and Jahnke, K. and Kermiche, S. and Kiessling, A. and Kilbinger, M. and Kitching, T. and Kümmel, M. and Kunz, M. and Kurki-Suonio, H. and Ligori, S. and Lilje, P. B. and Lloro, I. and Marggraf, O. and Markovic, K. and Marulli, F. and Meneghetti, M. and Meylan, G. and Moresco, M. and Moscardini, L. and Munari, E. and Niemi, S. M. and Padilla, C. and Paltani, S. and Pasian, F. and Pedersen, K. and Pettorino, V. and Pires, S. and Poncet, M. and Popa, L. and Raison, F. and Rhodes, J. and Rossetti, E. and Saglia, R. and Sartoris, B. and Schneider, P. and Secroun, A. and Seidel, G. and Sirignano, C. and Sirri, G. and Stanco, L. and Starck, J.-L. and Tallada-Crespí, P. and Tavagnacco, D. and Taylor, A. N. and Tereno, I. and Toledo-Moreo, R. and Torradeflot, F. and Valenziano, L. and Wang, Y. and Zamorani, G. and Zoubian, J. and Andreon, S. and Baldi, M. and Camera, S. and Cardone, V. F. and Fabbian, G. and Polenta, G. and Renzi, A. and Joachimi, B. and Hall, A. and Loureiro, A. and Sellentin, E. (2022) Euclid: Covariance of weak lensing pseudo-C_ℓ estimates. Calculation, comparison to simulations, and dependence on survey geometry. Astronomy and Astrophysics, 660 . Art. No. A114. ISSN 0004-6361. doi:10.1051/0004-6361/202142908.

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An accurate covariance matrix is essential for obtaining reliable cosmological results when using a Gaussian likelihood. In this paper we study the covariance of pseudo-C_ℓ estimates of tomographic cosmic shear power spectra. Using two existing publicly available codes in combination, we calculate the full covariance matrix, including mode-coupling contributions arising from both partial sky coverage and non-linear structure growth. For three different sky masks, we compare the theoretical covariance matrix to that estimated from publicly available N-body weak lensing simulations, finding good agreement. We find that as a more extreme sky cut is applied, a corresponding increase in both Gaussian off-diagonal covariance and non-Gaussian super-sample covariance is observed in both theory and simulations, in accordance with expectations. Studying the different contributions to the covariance in detail, we find that the Gaussian covariance dominates along the main diagonal and the closest off-diagonals, but farther away from the main diagonal the super-sample covariance is dominant. Forming mock constraints in parameters that describe matter clustering and dark energy, we find that neglecting non-Gaussian contributions to the covariance can lead to underestimating the true size of confidence regions by up to 70 per cent. The dominant non-Gaussian covariance component is the super-sample covariance, but neglecting the smaller connected non-Gaussian covariance can still lead to the underestimation of uncertainties by 10–20 per cent. A real cosmological analysis will require marginalisation over many nuisance parameters, which will decrease the relative importance of all cosmological contributions to the covariance, so these values should be taken as upper limits on the importance of each component.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Upham, R. E.0000-0002-4172-3358
Rhodes, J.0000-0002-4485-8549
Wang, Y.0000-0002-4749-2984
Additional Information:© ESO 2022. Article published by EDP Sciences. Received 14 December 2021; Accepted 5 February 2022; Published online 22 April 2022. We thank the internal and external referees and colleagues for helpful feedback, which has improved the manuscript. This work would not have been possible without the contributions to the community from the developers of NaMaster (Alonso et al. 2019; García-García et al. 2019), CosmoLike (Krause & Eifler 2017; Fang et al. 2020) and the simulations of Takahashi et al. (2017). REU acknowledges a studentship from the UK Science and Technology Facilities Council. The Euclid Consortium acknowledges the European Space Agency and a number of agencies and institutes that have supported the development of Euclid, in particular the Academy of Finland, the Agenzia Spaziale Italiana, the Belgian Science Policy, the Canadian Euclid Consortium, the French Centre National d’Etudes Spatiales, the Deutsches Zentrum für Luft- und Raumfahrt, the Danish Space Research Institute, the Fundação para a Ciência e a Tecnologia, the Ministerio de Economia y Competitividad, the National Aeronautics and Space Administration, the National Astronomical Observatory of Japan, the Netherlandse Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the Romanian Space Agency, the State Secretariat for Education, Research and Innovation (SERI) at the Swiss Space Office (SSO), and the United Kingdom Space Agency. A complete and detailed list is available on the Euclid web site (
Group:Infrared Processing and Analysis Center (IPAC)
Funding AgencyGrant Number
Science and Technology Facilities Council (STFC)UNSPECIFIED
European Space Agency (ESA)UNSPECIFIED
Academy of FinlandUNSPECIFIED
Agenzia Spaziale Italiana (ASI)UNSPECIFIED
Belgian Federal Science Policy Office (BELSPO)UNSPECIFIED
Canadian Euclid ConsortiumUNSPECIFIED
Centre National d'Études Spatiales (CNES)UNSPECIFIED
Deutsches Zentrum für Luft- und Raumfahrt (DLR)UNSPECIFIED
Danish Space Research InstituteUNSPECIFIED
Fundação para a Ciência e a Tecnologia (FCT)UNSPECIFIED
Ministerio de Economía y Competitividad (MINECO)UNSPECIFIED
National Astronomical Observatory of JapanUNSPECIFIED
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)UNSPECIFIED
Norwegian Space AgencyUNSPECIFIED
Romanian Space AgencyUNSPECIFIED
State Secretariat for Education, Research and Innovation (SERI)UNSPECIFIED
Swiss Space Office (SSO)UNSPECIFIED
United Kingdom Space Agency (UKSA)UNSPECIFIED
Subject Keywords:gravitational lensing: weak – methods: statistical – cosmology: observations
Record Number:CaltechAUTHORS:20220621-875563800
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Official Citation:Euclid: Covariance of weak lensing pseudo-Cℓ estimates - Calculation, comparison to simulations, and dependence on survey geometry. R. E. Upham, M. L. Brown, L. Whittaker, A. Amara, N. Auricchio, D. Bonino, E. Branchini, M. Brescia, J. Brinchmann, V. Capobianco, C. Carbone, J. Carretero, M. Castellano, S. Cavuoti, A. Cimatti, R. Cledassou, G. Congedo, L. Conversi, Y. Copin, L. Corcione, M. Cropper, A. Da Silva, H. Degaudenzi, M. Douspis, F. Dubath, C. A. J. Duncan, X. Dupac, S. Dusini, A. Ealet, S. Farrens, S. Ferriol, P. Fosalba, M. Frailis, E. Franceschi, M. Fumana, B. Garilli, B. Gillis, C. Giocoli, F. Grupp, S. V. H. Haugan, H. Hoekstra, W. Holmes, F. Hormuth, A. Hornstrup, K. Jahnke, S. Kermiche, A. Kiessling, M. Kilbinger, T. Kitching, M. Kümmel, M. Kunz, H. Kurki-Suonio, S. Ligori, P. B. Lilje, I. Lloro, O. Marggraf, K. Markovic, F. Marulli, M. Meneghetti, G. Meylan, M. Moresco, L. Moscardini, E. Munari, S. M. Niemi, C. Padilla, S. Paltani, F. Pasian, K. Pedersen, V. Pettorino, S. Pires, M. Poncet, L. Popa, F. Raison, J. Rhodes, E. Rossetti, R. Saglia, B. Sartoris, P. Schneider, A. Secroun, G. Seidel, C. Sirignano, G. Sirri, L. Stanco, J.-L. Starck, P. Tallada-Crespí, D. Tavagnacco, A. N. Taylor, I. Tereno, R. Toledo-Moreo, F. Torradeflot, L. Valenziano, Y. Wang, G. Zamorani, J. Zoubian, S. Andreon, M. Baldi, S. Camera, V. F. Cardone, G. Fabbian, G. Polenta, A. Renzi, B. Joachimi, A. Hall, A. Loureiro and E. Sellentin. A&A, 660 (2022) A114; DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115219
Deposited By: Tony Diaz
Deposited On:22 Jun 2022 19:47
Last Modified:28 Jun 2022 18:04

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