Euclid preparation: LXII. Simulations and non-linearities beyond Lambda cold dark matter. 1. Numerical methods and validation

Adamek, J.; Fiorini, B.; Baldi, M.; Brando, G.; Breton, M. -A.; Hassani, F.; Koyama, K.; Le Brun, A. M. C.; R??cz, G.; Winther, H. -A.; Casalino, A.; Hern??ndez-Aguayo, C.; Li, B.; Potter, D.; Altamura, E.; Carbone, C.; Giocoli, C.; Mota, D. F.; Pourtsidou, A.; Sakr, Z.; Vernizzi, F.; Amara, A.; Andreon, S.; Auricchio, N.; Baccigalupi, C.; Bardelli, S.; Battaglia, P.; Bonino, D.; Branchini, E.; Brescia, M.; Brinchmann, J.; Caillat, A.; Camera, S.; Capobianco, V.; Cardone, V. F.; Carretero, J.; Casas, S.; Castander, F. J.; Castellano, M.; Castignani, G.; Cavuoti, S.; Cimatti, A.; Colodro-Conde, C.; Congedo, G.; Conselice, C. J.; Conversi, L.; Copin, Y.; Courbin, F.; Courtois, H. M.; Silva, A. D.; Degaudenzi, H.; De Lucia, G.; Douspis, M.; Dubath, F.; Dupac, X.; Dusini, S.; Farina, M.; Farrens, S.; Ferriol, S.; Fosalba, P.; Frailis, M.; Franceschi, E.; Fumana, M.; Galeotta, S.; Gillis, B.; G??mez-Alvarez, P.; Grazian, A.; Grupp, F.; Guzzo, L.; Haugan, S. V. H.; Holmes, W.; Hormuth, F.; Hornstrup, A.; Ili??, S.; Jahnke, K.; Jhabvala, M.; Joachimi, B.; Keih??nen, E.; Kermiche, S.; Kiessling, A.; Kilbinger, M.; Kubik, B.; K??mmel, M.; Kunz, M.; Kurki-Suonio, H.; Ligori, S.; Lilje, P. B.; Lindholm, V.; Lloro, I.; Mainetti, G.; Maiorano, E.; Mansutti, O.; Marggraf, O.; Markovic, K.; Martinelli, M.; Martinet, N.; Marulli, F.; Massey, R.; Medinaceli, E.; Mei, S.; Melchior, M.; Mellier, Y.; Meneghetti, M.; Merlin, E.; Meylan, G.; Moresco, M.; Moscardini, L.; Neissner, C.; Niemi, S. -M.; Padilla, C.; Paltani, S.; Pasian, F.; Pedersen, K.; Percival, W. J.; Pettorino, V.; Pires, S.; Polenta, G.; Poncet, M.; Popa, L. A.; Pozzetti, L.; Raison, F.; Renzi, A.; Rhodes, J.; Riccio, G.; Romelli, E.; Roncarelli, M.; Saglia, R.; S??nchez, A. G.; Sapone, D.; Sartoris, B.; Schirmer, M.; Schrabback, T.; Secroun, A.; Seidel, G.; Serrano, S.; Sirignano, C.; Sirri, G.; Stanco, L.; Steinwagner, J.; Tallada-Cresp??, P.; Tavagnacco, D.; Tereno, I.; Toledo-Moreo, R.; Torradeflot, F.; Tutusaus, I.; Valentijn, E. A.; Valenziano, L.; Vassallo, T.; Verdoe Kleijn, G.; Veropalumbo, A.; Wang, Y.; Weller, J.; Zamorani, G.; Zucca, E.; Biviano, A.; Burigana, C.; Calabrese, M.; Di Ferdinando, D.; Escarti Vigo, J. A.; Fabbian, G.; Finelli, F.; Gracia-Carpio, J.; Matthew, S.; Mauri, N.; Pezzotta, A.; P??ntinen, M.; Scottez, V.; Tenti, M.; Viel, M.; Wiesmann, M.; Akrami, Y.; Allevato, V.; Anselmi, S.; Archidiacono, M.; Atrio-Barandela, F.; Balaguera-Antolinez, A.; Ballardini, M.; Blanchard, A.; Blot, L.; B??hringer, H.; Borgani, S.; Bruton, S.; Cabanac, R.; Calabro, A.; Camacho Quevedo, B.; Ca??as-Herrera, G.; Cappi, A.; Caro, F.; Carvalho, C. S.; Castro, T.; Chambers, K. C.; Contarini, S.; Cooray, A. R.; Desprez, G.; D??az-S??nchez, A.; Diaz, J. J.; Di Domizio, S.; Dole, H.; Escoffier, S.; Ferrari, A. G.; Ferreira, P. G.; Ferrero, I.; Finoguenov, A.; Fornari, F.; Gabarra, L.; Ganga, K.; Garc??a-Bellido, J.; Gasparetto, T.; Gautard, V.; Gaztanaga, E.; Giacomini, F.; Gianotti, F.; Gozaliasl, G.; Gutierrez, C. M.; Hall, A.; Hildebrandt, H.; Hjorth, J.; Jimene Mu??oz, A.; Joudaki, S.; Kajava, J. J. E.; Kansal, V.; Karagiannis, D.; Kirkpatrick, C. C.; Kruk, S.; Graet, J. L.; Legrand, L.; Lesgourgues, J.; Liaudat, T. I.; Loureiro, A.; Maggio, G.; Magliocchetti, M.; Mannucci, F.; Maoli, R.; Martins, C. J. A. P.; Maurin, L.; Metcalf, R. B.; Migliaccio, M.; Miluzio, M.; Monaco, P.; Montoro, A.; Mora, A.; Moretti, C.; Morgante, G.; Nadathur, S.; Patrizii, L.; Popa, V.; Reimberg, P.; Risso, I.; Rocci, P. -F.; Sahl??n, M.; Sarpa, E.; Schneider, A.; Sereno, M.; Silvestri, A.; Spurio Mancini, A.; Tanidis, K.; Tao, C.; Tessore, N.; Testera, G.; Teyssier, R.; Toft, S.; Tosi, S.; Troja, A.; Tucci, M.; Valieri, C.; Valiviita, J.; Vergani, D.; Verza, G.; Vielzeuf, P.; Walton, N. A.

doi:10.1051/0004-6361/202452180

To constrain cosmological models beyond ACDM, the development of the Euclid analysis pipeline requires simulations that capture the non-linear phenomenology of such models. We present an overview of numerical methods and N-body simulation codes developed to study the non-linear regime of structure formation in alternative dark energy and modified gravity theories. We review a variety of numerical techniques and approximations employed in cosmological N-body simulations to model the complex phenomenology of scenarios beyond ACDM. This includes discussions on solving non-linear field equations, accounting for fifth forces, and implementing screening mechanisms. Furthermore, we conduct a code comparison exercise to assess the reliability and convergence of different simulation codes across a range of models. Our analysis demonstrates a high degree of agreement among the outputs of different simulation codes, typically within 2% for the predicted modification of the matter power spectrum and within 4% for the predicted modification of the halo mass function, although some approximations degrade accuracy a bit further. This provides confidence in current numerical methods of modelling cosmic structure formation beyond ACDM. We highlight recent advances made in simulating the non-linear scales of structure formation, which are essential for leveraging the full scientific potential of the forthcoming observational data from the Euclid mission.