Euclid preparation. LXXXVII. Non-Gaussianity of two-point statistics likelihood: Precise analysis of the matter power spectrum distribution

Euclid Collaboration; Bel, J.; Gouyou Beauchamps, S.; Baratta, P.; Blot, L.; Carbone, C.; Corasaniti, P.-S.; Sefusatti, E.; Escoffier, S.; Gillard, W.; Amara, A.; Andreon, S.; Auricchio, N.; Baccigalupi, C.; Baldi, M.; Bardelli, S.; Battaglia, P.; Biviano, A.; Branchini, E.; Brescia, M.; Brinchmann, J.; Camera, S.; Cañas-Herrera, G.; Capobianco, V.; Cardone, V. F.; Carretero, J.; Casas, S.; Castellano, M.; Castignani, G.; Cavuoti, S.; Chambers, K. C.; Cimatti, A.; Colodro-Conde, C.; Congedo, G.; Conselice, C. J.; Conversi, L.; Copin, Y.; Costille, A.; Courbin, F.; Courtois, H. M.; Da Silva, A.; Degaudenzi, H.; de la Torre, S.; De Lucia, G.; Dubath, F.; Duncan, C. A. J.; Dupac, X.; Farina, M.; Farinelli, R.; Faustini, F.; Ferriol, S.; Finelli, F.; Fourmanoit, N.; Frailis, M.; Franceschi, E.; Fumana, M.; Galeotta, S.; George, K.; Gillis, B.; Giocoli, C.; Gracia-Carpio, J.; Grazian, A.; Grupp, F.; Guzzo, L.; Haugan, S. V. H.; Holmes, W.; Hormuth, F.; Hornstrup, A.; Jahnke, K.; Jhabvala, M.; Joachimi, B.; Keihänen, E.; Kermiche, S.; Kubik, B.; Kunz, M.; Kurki-Suonio, H.; Le Brun, A. M. C.; Ligori, S.; Lilje, P. B.; Lindholm, V.; Lloro, I.; Mainetti, G.; Maino, D.; Maiorano, E.; Mansutti, O.; Marggraf, O.; Markovic, K.; Martinelli, M.; Martinet, N.; Marulli, F.; Massey, R.; Medinaceli, E.; Mellier, Y.; Meneghetti, M.; Merlin, E.; Meylan, G.; Mora, A.; 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.; Raison, F.; Renzi, A.; Rhodes, J.; Riccio, G.; Rizzo, F.; Romelli, E.; Roncarelli, M.; Saglia, R.; Sakr, Z.; Sánchez, A. G.; Sapone, D.; Sartoris, B.; Schneider, P.; Schrabback, T.; Scodeggio, M.; Secroun, A.; Seidel, G.; Seiffert, M.; Serrano, S.; Simon, P.; Sirignano, C.; Sirri, G.; Stanco, L.; Steinwagner, J.; Tallada-Crespí, P.; Taylor, A. N.; Tereno, I.; Tessore, N.; Toft, S.; Toledo-Moreo, R.; Torradeflot, F.; Tutusaus, I.; Valenziano, L.; Valiviita, J.; Vassallo, T.; Veropalumbo, A.; Wang, Y.; Weller, J.; Zamorani, G.; Zucca, E.; Ballardini, M.; Bozzo, E.; Burigana, C.; Cabanac, R.; Calabrese, M.; Di Ferdinando, D.; Escartin Vigo, J. A.; Gabarra, L.; Martín-Fleitas, J.; Matthew, S.; Mauri, N.; Metcalf, R. B.; Pezzotta, A.; Pöntinen, M.; Porciani, C.; Risso, I.; Scottez, V.; Sereno, M.; Tenti, M.; Viel, M.; Wiesmann, M.; Akrami, Y.; Alvi, S.; Andika, I. T.; Anselmi, S.; Archidiacono, M.; Atrio-Barandela, F.; Bertacca, D.; Bethermin, M.; Blanchard, A.; Borgani, S.; Brown, M. L.; Bruton, S.; Calabro, A.; Camacho Quevedo, B.; Caro, F.; Carvalho, C. S.; Castro, T.; Cogato, F.; Conseil, S.; Contarini, S.; Cooray, A. R.; Davini, S.; Desprez, G.; Díaz-Sánchez, A.; Diaz, J. J.; Di Domizio, S.; Diego, J. M.; Enia, A.; Fang, Y.; Ferrari, A. G.; Finoguenov, A.; Franco, A.; Ganga, K.; García-Bellido, J.; Gasparetto, T.; Gautard, V.; Gaztanaga, E.; Giacomini, F.; Gianotti, F.; Gozaliasl, G.; Guidi, M.; Gutierrez, C. M.; Hall, A.; Hernández-Monteagudo, C.; Hildebrandt, H.; Hjorth, J.; Kajava, J. J. E.; Kang, Y.; Kansal, V.; Karagiannis, D.; Kiiveri, K.; Kirkpatrick, C. C.; Kruk, S.; Lattanzi, M.; Le Graet, J.; Legrand, L.; Lembo, M.; Lepori, F.; Leroy, G.; Lesci, G. F.; Lesgourgues, J.; Leuzzi, L.; Liaudat, T. I.; Macias-Perez, J.; Maggio, G.; Magliocchetti, M.; Mannucci, F.; Maoli, R.; Martins, C. J. A. P.; Maurin, L.; Miluzio, M.; Monaco, P.; Moretti, C.; Morgante, G.; Nadathur, S.; Naidoo, K.; Navarro-Alsina, A.; Nesseris, S.; Pagano, L.; Passalacqua, F.; Paterson, K.; Patrizii, L.; Pisani, A.; Potter, D.; Quai, S.; Radovich, M.; Reimberg, P.; Rocci, P.-F.; Rodighiero, G.; Sacquegna, S.; Sahlén, M.; Sanders, D. B.; Sarpa, E.; Schneider, A.; Sciotti, D.; Sellentin, E.; Smith, L. C.; Sorce, J. G.; Tanidis, K.; Tao, C.; Testera, G.; Teyssier, R.; Tosi, S.; Troja, A.; Tucci, M.; Valieri, C.; Venhola, A.; Vergani, D.; Vernizzi, F.; Verza, G.; Vielzeuf, P.; Walton, N. A.

doi:10.1051/0004-6361/202556642

Published April 2026 | Version Published

Journal Article Open

Euclid preparation. LXXXVII. Non-Gaussianity of two-point statistics likelihood: Precise analysis of the matter power spectrum distribution

1. Centre de Physique Théorique
2. Institut d'Estudis Espacials de Catalunya
3. Institute of Space Sciences
4. Center for Particle Physics of Marseilles
5. Aix-Marseille University
6. University of Tokyo
7. Sorbonne University
8. Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano
9. Institut d'Astrophysique de Paris
10. Trieste Astronomical Observatory
11. Institute for Fundamental Physics of the Universe
12. INFN Sezione di Trieste
13. University of Surrey
14. Brera Astronomical Observatory
15. INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129, Bologna, Italy
16. International School for Advanced Studies
17. University of Bologna
18. INFN Sezione di Bologna
19. University of Genoa
20. INFN Sezione di Genova
21. University of Naples Federico II
22. Astronomical Observatory of Capodimonte
23. University of Porto
24. European Southern Observatory
25. University of Turin
26. INFN Sezione di Torino
27. Osservatorio Astrofisico di Torino
28. European Space Research and Technology Centre
29. Leiden University
30. Astronomical Observatory of Rome
31. INFN Sezione di Roma I
32. Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
33. Port d'Informació Científica
34. RWTH Aachen University
35. INFN Sezione di Napoli
36. University of Hawaii at Manoa
37. Instituto de Astrofísica de Canarias
38. University of Edinburgh
39. University of Manchester
40. European Space Research Institute
41. European Space Astronomy Centre
42. Claude Bernard University Lyon 1
43. French National Centre for Scientific Research
44. University of Barcelona
45. Institució Catalana de Recerca i Estudis Avançats
46. UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622, Villeurbanne, France
47. University of Lisbon
48. University of Geneva
49. Institute for Space Astrophysics and Planetology
50. Agenzia Spaziale Italiana
51. Ludwig-Maximilians-Universität München
52. Max Planck Institute for Extraterrestrial Physics
53. Osservatorio Astronomico di Padova
54. University of Milan
55. INFN Sezione di Milano
56. University of Oslo
57. Jet Propulsion Lab
58. Felix Hormuth Engineering, Goethestr. 17, 69181, Leimen, Germany
59. Technical University of Denmark
60. University of Copenhagen
61. Max Planck Institute for Astronomy
62. Goddard Space Flight Center
63. University College London
64. University of Helsinki
65. Helsinki Institute of Physics
66. Square Kilometre Array Organisation
67. Centre de Calcul de l'Institut National de Physique Nucléaire et de Physique des Particules
68. University of Bonn
69. Durham University
70. École Polytechnique Fédérale de Lausanne
71. Telespazio UK S.L. for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692, Madrid, Spain
72. Institute for High Energy Physics
73. University of Waterloo
74. Perimeter Institute
75. University of Paris
76. Centre National d'Études Spatiales
77. Institute of Space Science
78. University of Padua
79. INFN Sezione di Padova
80. Heidelberg University
81. Research Institute in Astrophysics and Planetology
82. Université St Joseph; Faculty of Sciences, Beirut, Lebanon
83. University of Chile
84. Universität Innsbruck
85. Satlantis, University Science Park, Sede Bld, 48940, Leioa-Bilbao, Spain
86. Cosmic Dawn Center (DAWN)
87. Polytechnic University of Cartagena
88. Infrared Processing and Analysis Center
89. University of Ferrara
90. INFN Sezione di Ferrara
91. Istituto di Radioastronomia di Bologna
92. Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020, Nus (Aosta Valley), Italy
93. University of Oxford
94. Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692, Madrid, Spain
95. Groupe Institut supérieur d'agriculture de Lille
96. ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
97. Institute for Theoretical Physics
98. Case Western Reserve University
99. Technical University of Munich
100. Max Planck Institute for Astrophysics
101. University of Salamanca
102. Observatory of Strasbourg
103. University of Trieste
104. California Institute of Technology
105. University of California, Irvine
106. University of Groningen
107. Institute of Physics of Cantabria
108. INFN Sezione di Lecce
109. University of Salento
110. INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100, Lecce, Italy
111. Astroparticle and Cosmology Laboratory
112. CEA Saclay
113. University of Portsmouth
114. Aalto University
115. University of La Laguna
116. Ruhr University Bochum
117. University of Turku
118. Serco for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692, Madrid, Spain
119. ARC Centre of Excellence for Dark Matter Particle Physics
120. Swinburne University of Technology
121. University of the Western Cape
122. University of Cambridge
123. University of Zurich
124. Institut de Recherche sur les Lois Fondamentales de l'Univers
125. Grenoble Institute of Technology
126. Arcetri Astrophysical Observatory
127. Sapienza University of Rome
128. Centre for Astrophysics of the University of Porto
129. Institut d'Astrophysique Spatiale
130. HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692, Madrid, Spain
131. Collurania Teramo Observatory
132. Uppsala University
133. University of Lille
134. Princeton University
135. University of Oulu
136. L'Institut de physique théorique
137. Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010, New York, NY, USA

We investigate the non-Gaussian features in the distribution of the matter power spectrum multipoles. Using the COVMOS method, we generated 100 000 mock realisations of dark matter density fields in both real and redshift space across multiple redshifts and cosmological models. We derived an analytical framework linking the non-Gaussianity of the power spectrum distribution to higher-order statistics of the density field, including the trispectrum and pentaspectrum. We explored the effect of redshift-space distortions, the geometry of the survey, the Fourier binning, the integral constraint, and the shot noise on the skewness of the distribution of the power spectrum measurements. Our results demonstrate that the likelihood of the estimated matter power spectrum significantly deviates from a Gaussian assumption on non-linear scales, particularly at low redshift. This departure is primarily driven by the pentaspectrum contribution, which dominates over the trispectrum at intermediate scales. We also examined the impact of the finiteness of the survey geometry in the context of the Euclid mission, and we find that both the shape of the survey and the integral constraint amplify the skewness.

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© The Authors 2026. Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Acknowledgement

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 Agenzia Spaziale Italiana, the Austrian Forschungsförderungsgesellschaft funded through BMK, the Belgian Science Policy, the Canadian Euclid Consortium, the Deutsches Zentrum für Luft- und Raumfahrt, the DTU Space and the Niels Bohr Institute in Denmark, the French Centre National d’Etudes Spatiales, the Fundação para a Ciência e a Tecnologia, the Hungarian Academy of Sciences, the Ministerio de Ciencia, Innovación y Universidades, the National Aeronautics and Space Administration, the National Astronomical Observatory of Japan, the Netherlandse Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the Research Council of Finland, 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 (www.euclid-ec.org). The project leading to this publication has received funding from Excellence Initiative of Aix-Marseille University -A*MIDEX, a French “Investissements d’Avenir” programme (AMX-19-IET-008 -IPhU). The DEMNUni-cov simulations were carried out in the framework of “The Dark Energy and Massive Neutrino Universe covariances” project, using the Tier-0 Intel OmniPath Cluster Marconi-A1 of the Centro Interuniversitario del Nord-Est per il Calcolo Elettronico (CINECA). We acknowledge a generous CPU and storage allocation by the Italian Super-Computing Resource Allocation (ISCRA) as well as from the coordination of the “Accordo Quadro MoU per lo svolgimento di attività congiunta di ricerca Nuove frontiere in Astrofisica: HPC e Data Exploration di nuova generazione”, together with storage from INFN-CNAF and INAF-IA2.

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Is new version of: Discussion Paper: arXiv:2511.08266 (arXiv)

European Space Agency

Submitted: 2025-07-29
Accepted: 2025-12-29
Available: 2026-03-30

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Caltech groups: Infrared Processing and Analysis Center (IPAC) , Division of Physics, Mathematics and Astronomy (PMA) , Physics Department
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Euclid preparation. LXXXVII. Non-Gaussianity of two-point statistics likelihood: Precise analysis of the matter power spectrum distribution

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