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

M. Knabenhans, J. Stadel, D. Potter, J. Dakin, S. Hannestad, T. Tram, S. Marelli, A. Schneider, R. Teyssier, P. Fosalba, S. Andreon, N. Auricchio, C. Baccigalupi, A. Balaguera-Antolínez, M. Baldi, S. Bardelli, P. Battaglia, R. Bender, A. Biviano, C. BodendorfE. Bozzo, E. Branchini, M. Brescia, C. Burigana, R. Cabanac, S. Camera, V. Capobianco, A. Cappi, C. Carbone, J. Carretero, C. S. Carvalho, R. Casas, S. Casas, M. Castellano, G. Castignani, S. Cavuoti, R. Cledassou, C. Colodro-Conde, G. Congedo, C. J. Conselice, L. Conversi, Y. Copin, L. Corcione, J. Coupon, H. M. Courtois, A. Da Silva, S. De La Torre, D. Di Ferdinando, C. A.J. Duncan, X. Dupac, G. Fabbian, S. Farrens, P. G. Ferreira, F. Finelli, M. Frailis, E. Franceschi, S. Galeotta, B. Garilli, C. Giocoli, G. Gozaliasl, J. Graciá-Carpio, F. Grupp, L. Guzzo, W. Holmes, F. Hormuth, H. Israel, K. Jahnke, E. Keihanen, S. Kermiche, C. C. Kirkpatrick, B. Kubik, M. Kunz, H. Kurki-Suonio, S. Ligori, P. B. Lilje, I. Lloro, D. Maino, O. Marggraf, K. Markovic, N. Martinet, F. Marulli, R. Massey, N. Mauri, S. Maurogordato, E. Medinaceli, M. Meneghetti, B. Metcalf, G. Meylan, M. Moresco, B. Morin, L. Moscardini, E. Munari, C. Neissner, S. M. Niemi, C. Padilla, S. Paltani, F. Pasian, L. Patrizii, V. Pettorino, S. Pires, G. Polenta, M. Poncet, F. Raison, A. Renzi, J. Rhodes, G. Riccio, E. Romelli, M. Roncarelli, R. Saglia, A. G. Sánchez, D. Sapone, P. Schneider, V. Scottez, A. Secroun, S. Serrano, C. Sirignano, G. Sirri, L. Stanco, F. Sureau, P. Tallada Crespí, A. N. Taylor, M. Tenti, I. Tereno, R. Toledo-Moreo, F. Torradeflot, L. Valenziano, J. Valiviita, T. Vassallo, M. Viel, Y. Wang, N. Welikala, L. Whittaker, A. Zacchei, E. Zucca

Research output: Contribution to journalArticlepeer-review

69 Scopus citations


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 w0waCDM+∑mν models between redshift z = 0 and z = 3 for spatial scales within the range $0.01 \, h\, {\rm Mpc}^{-1}\le k \le 10\, h\, {\rm Mpc}^{-1}$. 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 wa 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 $1{{\ \rm per\ cent}}$ or better for $0.01 \, h\, {\rm Mpc}^{-1}\le k \le 10\, h\, {\rm Mpc}^{-1}$ and z ≤ 3 compared to high-resolution dark-matter-only simulations. EuclidEmulator2 is publicly available at

Original languageEnglish (US)
Pages (from-to)2840-2869
Number of pages30
JournalMonthly Notices of the Royal Astronomical Society
Issue number2
StatePublished - Aug 1 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • cosmological parameters
  • large-scale structure of Universe
  • methods: numerical
  • methods: statistical


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