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Euclid preparation. IX. EuclidEmulator2 – power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations

Knabenhans, M. and Stadel, J. and Potter, D. and Dakin, J. and Hannestad, S. and Tram, T. and Marelli, S. and Schneider, A. and Teyssier, R. and Andreon, S. and Auricchio, N. and Baccigalupi, C. and Balaguera-Antolínez, A. and Baldi, M. and Bardelli, S. and Battaglia, P. and Bender, R. and Biviano, A. and Bodendorf, C. and Bozzo, E. and Branchini, E. and Brescia, M. and Burigana, C. and Cabanac, R. and Camera, S. and Capobianco, V. and Cappi, A. and Carbone, C. and Carretero, J. and Carvalho, C. S. and Casas, R. and Casas, S. and Castellano, M. and Castignani, G. and Cavuoti, S. and Cledassou, R. and Colodro-Conde, C. and Congedo, G. and Conselice, C. J. and Conversi, L. and Copin, Y. and Corcione, L. and Coupon, J. and Courtois, H. M. and Da Silva, A. and de la Torre, S. and Di Ferdinando, D. and Duncan, C. A. J. and Dupac, X. and Fabbian, G. and Farrens, S. and Ferreira, P. G. and Finelli, F. and Frailis, M. and Franceschi, E. and Galeotta, S. and Garilli, B. and Giocoli, C. and Gozaliasl, G. and Graciá-Carpio, J. and Grupp, F. and Guzzo, L. and Holmes, W. and Hormuth, F. and Israel, H. and Jahnke, K. and Keihanen, E. and Kermiche, S. and Kirkpatrick, C. C. and Kubik, B. and Kunz, M. and Kurki-Suonio, H. and Ligori, S. and Lilje, P. B. and Lloro, I. and Maino, D. and Marggraf, O. and Markovic, K. and Martinet, N. and Marulli, F. and Massey, R. and Mauri, N. and Maurogordato, S. and Medinaceli, E. and Meneghetti, M. and Metcalf, B. and Meylan, G. and Moresco, M. and Morin, B. and Moscardini, L. and Munari, E. and Neissner, C. and Niemi, S. M. and Padilla, C. and Paltani, S. and Pasian, F. and Patrizii, L. and Pettorino, V. and Pires, S. and Polenta, G. and Poncet, M. and Raison, F. and Renzi, A. and Rhodes, J. and Riccio, G. and Romelli, E. and Roncarelli, M. and Saglia, R. and Sánchez, A. G. and Sapone, D. and Schneider, P. and Scottez, V. and Secroun, A. and Serrano, S. and Sirignano, C. and Sirri, G. and Stanco, L. and Sureau, F. and Tallada Crespí, P. and Taylor, A. N. and Tenti, M. and Tereno, I. and Toledo-Moreo, R. and Torradeflot, F. and Valenziano, L. and Valiviita, J. and Vassallo, T. and Viel, M. and Wang, Y. and Welikala, N. and Whittaker, L. and Zacchei, A. and Zucca, E. (2021) Euclid preparation. IX. EuclidEmulator2 – power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations. Monthly Notices of the Royal Astronomical Society, 505 (2). pp. 2840-2869. ISSN 0035-8711. doi:10.1093/mnras/stab1366.

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We present a new, updated version of the EuclidEmulator (called EuclidEmulator2), a fast and accurate predictor for the nonlinear correction of the matter power spectrum. 2 per cent level accurate emulation is now supported in the eight-dimensional parameter space of w₀w_aCDM+∑m_ν models between redshift z = 0 and z = 3 for spatial scales within the range 0.01 h Mpc⁻¹ ≤ k ≤ 10 h Mpc⁻¹⁠. In order to achieve this level of accuracy, we have had to improve the quality of the underlying N-body simulations used as training data: (i) we use self-consistent linear evolution of non-dark matter species such as massive neutrinos, photons, dark energy, and the metric field, (ii) we perform the simulations in the so-called N-body gauge, which allows one to interpret the results in the framework of general relativity, (iii) we run over 250 high-resolution simulations with 30003 particles in boxes of 1(h⁻¹ Gpc)³ volumes based on paired-and-fixed initial conditions, and (iv) we provide a resolution correction that can be applied to emulated results as a post-processing step in order to drastically reduce systematic biases on small scales due to residual resolution effects in the simulations. We find that the inclusion of the dynamical dark energy parameter w_a significantly increases the complexity and expense of creating the emulator. The high fidelity of EuclidEmulator2 is tested in various comparisons against N-body simulations as well as alternative fast predictors such as HALOFIT, HMCode, and CosmicEmu. A blind test is successfully performed against the Euclid Flagship v2.0 simulation. Nonlinear correction factors emulated with EuclidEmulator2 are accurate at the level of 1 per cent or better for 0.01 h Mpc⁻¹ ≤ k ≤ 10 h Mpc⁻¹ and z ≤ 3 compared to high-resolution dark-matter-only simulations. EuclidEmulator2 is publicly available at

Item Type:Article
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URLURL TypeDescription Paper ItemEuclidEmulator2
de la Torre, S.0000-0002-0839-2884
Rhodes, J.0000-0002-4485-8549
Additional Information:© 2021 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Accepted 2021 May 2. Received 2021 May 2; in original form 2020 October 23. Published: 14 May 2021. MK acknowledges support from the Swiss National Science Foundation (SNF) grant 200020_149848 and the Forschungskredit of the University of Zurich, grant no. K-76102-01-01. Simulations were performed on the PizDaint supercomputer at the Swiss National Scientific supercomputing center CSCS and on the zBox4+ cluster at the University of Zurich. The Euclid Consortium acknowledges 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 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 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 ( Data Availability: The data underlying this article will be shared on reasonable request to the corresponding author.
Group:Infrared Processing and Analysis Center (IPAC)
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)200020_149848
University of ZurichK-76102-01-01
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
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)UNSPECIFIED
Norwegian Space AgencyUNSPECIFIED
Romanian Space AgencyUNSPECIFIED
State Secretariat for Education, Research and Innovation (SER)UNSPECIFIED
Swiss Space Office (SSO)UNSPECIFIED
United Kingdom Space Agency (UKSA)UNSPECIFIED
Subject Keywords:methods: numerical – methods: statistical – cosmological parameters – large-scale structure of Universe
Issue or Number:2
Record Number:CaltechAUTHORS:20201201-073034447
Persistent URL:
Official Citation:Euclid Collaboration, M Knabenhans, et. al., Euclid preparation: IX. EuclidEmulator2 – power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations, Monthly Notices of the Royal Astronomical Society, Volume 505, Issue 2, August 2021, Pages 2840–2869,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106852
Deposited By: Tony Diaz
Deposited On:02 Dec 2020 21:33
Last Modified:07 Feb 2022 17:25

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