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The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics

Eleonora Di Valentino Orcid Logo, Jackson Levi Said, Adam Riess, Agnieszka Pollo, Vivian Poulin, Adrià Gómez-Valent, Amanda Weltman, Antonella Palmese, Caroline D. Huang, Carsten van de Bruck, Chandra Shekhar Saraf, Cheng-Yu Kuo, Cora Uhlemann, Daniela Grandón, Dante Paz, Dominique Eckert, Elsa M. Teixeira, Emmanuel N. Saridakis, Eoin Ó Colgáin, Florian Beutler, Florian Niedermann, Francesco Bajardi, Gabriela Barenboim, Giulia Gubitosi, Ilaria Musella, Indranil Banik, Istvan Szapudi, Jack Singal, Jaume Haro Cases, Jens Chluba, Jesús Torrado, Jurgen Mifsud, Karsten Jedamzik, Khaled Said, Konstantinos Dialektopoulos, Laura Herold, Leandros Perivolaropoulos, Lei Zu, Lluís Galbany, Louise Breuval, Luca Visinelli, Luis A. Escamilla, Luis A. Anchordoqui, M.M. Sheikh-Jabbari, Margherita Lembo, Maria Giovanna Dainotti, Maria Vincenzi, Marika Asgari, Martina Gerbino, Matteo Forconi, Michele Cantiello, Michele Moresco, Micol Benetti, Nils Schöneberg, Özgür Akarsu, Rafael C. Nunes, Reginald Christian Bernardo, Ricardo Chávez, Richard I. Anderson, Richard Watkins, Salvatore Capozziello, Siyang Li, Sunny Vagnozzi, Supriya Pan, Tommaso Treu, Vid Irsic, Will Handley, William Giarè, Yukei Murakami, Abdolali Banihashemi, Adèle Poudou, Alan Heavens, Alan Kogut, Alba Domi, Aleksander Łukasz Lenart, Alessandro Melchiorri, Alessandro Vadalà, Alexandra Amon, Alexander Bonilla Rivera, Alexander Reeves, Alexander Zhuk, Alfio Bonanno, Ali Övgün, Alice Pisani, Alireza Talebian, Amare Abebe, Amin Aboubrahim, Ana Luisa González Morán, András Kovács, Andreas Lymperis, Andreas Papatriantafyllou, Andrew R. Liddle, Andronikos Paliathanasis, Andrzej Borowiec, Anil Kumar Yadav, Anita Yadav, Anjan Ananda Sen, Anjitha John William, Anne Christine Davis, Anowar J. Shajib, Anthony Walters, Anto Idicherian Lonappan, Anton Chudaykin, Antonio Capodagli, Antonio da Silva, Antonio De Felice, Antonio Racioppi, Araceli Soler Oficial, Ariadna Montiel, Arianna Favale, Armando Bernui, Arrianne Crystal Velasco, Asta Heinesen, Athanasios Bakopoulos, Athanasios Chatzistavrakidis, Bahman Khanpour, Bangalore S. Sathyaprakash, Bartek Zgirski, Benjamin L’Huillier, Benoit Famaey, Bhuvnesh Jain, Bing Zhang, Biswajit Karmakar, Branko Dragovich, Brooks Thomas, Carlos Correa, Carlos G. Boiza, Catarina Marques, Celia Escamilla-Rivera, Charalampos Tzerefos, Chi Zhang, Chiara De Leo, Christian Pfeifer, Christine Lee, Christo Venter, Cláudio Gomes, Clecio Roque De bom, Cristian Moreno-Pulido, Damianos Iosifidis, Dan Grin, Daniel Blixt, Dan Scolnic, Daniele Oriti, Daria Dobrycheva, Dario Bettoni, David Benisty, David Fernández-Arenas, David L. Wiltshire, David Sanchez Cid, David Tamayo, David Valls-Gabaud, Davide Pedrotti, Deng Wang, Denitsa Staicova, Despoina Totolou, Diego Rubiera-Garcia, Dinko Milaković, Dominic W. Pesce, Dominique Sluse, Duško Borka, Ebrahim Yusofi, Elena Giusarma, Elena Terlevich, Elena Tomasetti, Elias C. Vagenas, Elisa Fazzari, Elisa G.M. Ferreira, Elvis Barakovic, Emanuela Dimastrogiovanni, Emil Brinch Holm, Emil Mottola, Emre Özülker, Enrico Specogna, Enzo Brocato, Erik Jensko, Erika Antonette Enriquez, Esha Bhatia, Fabio Bresolin, Felipe Avila, Filippo Bouchè, Flavio Bombacigno, Fotios K. Anagnostopoulos, Francesco Pace, Francesco Sorrenti, Francisco S.N. Lobo, Frédéric Courbin, Frode K. Hansen, Greg Sloan, Gabriel Farrugia, Gabriel Lynch, Gabriela Garcia-Arroyo, Gabriella Raimondo, Gaetano Lambiase, Gagandeep S. Anand, Gaspard Poulot, Genly Leon, Gerasimos Kouniatalis, Germano Nardini, Géza Csörnyei, Giacomo Galloni, Giada Bargiacchi, Giannis Papagiannopoulos, Giovanni Montani, Giovanni Otalora, Giulia De Somma, Giuliana Fiorentino, Giuseppe Fanizza, Giuseppe Gaetano Luciano, Giuseppe Sarracino, Gonzalo J. Olmo, Goran S. Djordjević, Guadalupe Cañas-Herrera, Hanyu Cheng, Harry Desmond, Hassan Abdalla, Houzun Chen, Hsu-Wen Chiang, Hume A. Feldman, Hussain Gohar, Ido Ben-Dayan, Ignacio Sevilla-Noarbe, Ignatios Antoniadis, Ilim Cimdiker, Inês S. Albuquerque, Ioannis D. Gialamas, Ippocratis Saltas, Iryna Vavilova, Isidro Gómez-Vargas, Ismael Ayuso, Ismailov Nariman Zeynalabdi, Ivan De Martino, Ivonne Zavala Carrasco Orcid Logo, J. Alberto Vázquez, Jacobo Asorey, Janusz Gluza, Javier Rubio, Jenny G. Sorce, Jenny Wagner, Jeremy Sakstein, Jessica Santiago, Jim Braatz, Joan Solà Peracaula, John Blakeslee, John Webb, Jose A.R. Cembranos, José Pedro Mimoso, Joseph Jensen, Juan García-Bellido, Judit Prat, Kathleen Sammut, Kay Lehnert, Keith R. Dienes, Kishan Deka, Konrad Kuijken, Krishna Naidoo, László Árpád Gergely, Laur Järv, Laura Mersini-Houghton, Leila L. Graef, Léo Vacher, Levon Pogosian, Lilia Anguelova, Lindita Hamolli, Lu Yin, Luca Caloni, Luca Izzo, Lucas Macri, Luis E. Padilla, Luz Ángela García, Maciej Bilicki, Mahdi Najafi, Manolis Plionis, Manuel Gonzalez-Espinoza, Manuel Hohmann, Marcel A. van der Westhuizen, Marcella Marconi, Marcin Postolak, Marco de Cesare, Marco Regis, Marek Biesiada, Maret Einasto, Margus Saal, Maria Caruana, Maria Petronikolou, Mariam Bouhmadi-López, Mariana Melo, Mariaveronica De Angelis, Marie-Noëlle Célérier, Marina Cortês, Mark Reid, Markus Michael Rau, Martin S. Sloth, Martti Raidal, Masahiro Takada, Masoume Reyhani, Massimiliano Romanello, Massimo Marengo, Mathias Garny, Matías Leizerovich, Matteo Martinelli, Matteo Tagliazucchi, Mehmet Demirci, Miguel A.S. Pinto, Miguel A. Sabogal, Miguel A. García-Aspeitia, Milan Milošević, Mina Ghodsi, Mustapha Ishak, Nelson J. Nunes, Nick Samaras, Nico Hamaus, Nico Schuster, Nicola Borghi, Nicola Deiosso, Nicola Tamanini, Nicolao Fornengo, Nihan Katırcı, Nikolaos E. Mavromatos, Nicholas Petropoulos, Nikolina Šarčević, Nils A. Nilsson, Nima Khosravi, Noemi Frusciante, Octavian Postavaru, Oem Trivedi, Oleksii Sokoliuk, Olga Mena, Paloma Morilla, Paolo Campeti, Paolo Salucci, Paula Boubel, Paweł Bielewicz, Pekka Heinämäki, Petar Suman, Petros Asimakis, Pierros Ntelis, Pran Nath, Predrag Jovanović, Purba Mukherjee, Radosław Wojtak, Rafaela Gsponer, Rafid H. Dejrah, Rahul Shah, Rasmi Hajjar, Rebecca Briffa, Rebecca Habas, Reggie C. Pantig, Renier Mendoza, Riccardo Della Monica, Richard Stiskalek, Rishav Roshan, Rita B. Neves, Roberto Molinaro, Roberto Terlevich, Rocco D’Agostino, Rodrigo Sandoval-Orozco, Ronaldo C. Batista, Ruchika, Ruth Lazkoz, Saeed Rastgoo, Sahar Mohammadi, Salvatore Samuele Sirletti, Sandeep Haridasu, Sanjay Mandal, Saurya Das, Sebastian Bahamonde, Sebastian Grandis, Sebastian Trojanowski, Sergei D. Odintsov, Sergij Mazurenko, Shahab Joudaki, Sherry H. Suyu, Shouvik Roy Choudhury, Shruti Bhatporia, Shun-Sheng Li, Simeon Bird, Simon Birrer, Simone Paradiso, Simony Santos da Costa, Sofia Contarini, Sophie Henrot-Versillé, Spyros Basilakos, Stefano Casertano, Stefano Gariazzo, Stylianos A. Tsilioukas, Surajit Kalita, Suresh Kumar, Susana J. Landau, Sveva Castello, Swayamtrupta Panda, Tanja Petrushevska, Thanasis Karakasis, Thejs Brinckmann, Tiago B. Gonçalves, Tiziano Schiavone, Tom Abel, Tomi Koivisto, Torsten Bringmann, Umut Demirbozan, Utkarsh Kumar, Valerio Marra, Maurice H.P.M. van Putten, Vasileios Kalaitzidis, Vasiliki A. Mitsou, Vasilios Zarikas, Vedad Pasic, Venus Keus, Verónica Motta, Vesna Borka Jovanović, Víctor H. Cárdenas, Vincenzo Ripepi, Vincenzo Salzano, Violetta Impellizzeri, Vitor da Fonseca, Vittorio Ghirardini, Vladas Vansevičius, Weiqiang Yang, Wojciech Hellwing, Xin Ren, Yu-Min Hu, Yuejia Zhai, Abdul Malik Sultan, Abdurakhmon Nosirov, Adrienn Pataki, Alessandro Santoni, Aliya Batool, Amlan Chakraborty, Aneta Wojnar, Arman Tursunov, Avik De, Ayush Hazarika, Baojiu Li, Benjamin Bose, Bivudutta Mishra, Bobomurat Ahmedov, Claudia Scóccola, Crescenzo Tortora, D’Arcy Kenworthy, Daniel E. Holz, David F. Mota, David S. Pereira, Devon M. Williams, Dillon Brout, Dong Ha Lee, Eduardo Guendelman, Edward Olex, Emanuelly Silva, Emre Onur Kahya, Eva-Maria Mueller, Felipe Andrade-Oliveira, Feven Markos Hunde, F.R. Joaquim, Florian Pacaud, Francis-Yan Cyr-Racine, F. Pozo Nuñez, Gábor Rácz, Gene Carlo Belinario, Geraint F. Lewis, Gergely Dálya, Giorgio Laverda, Guido Risaliti, Guillermo Franco-Abellán, Hayden Zammit, Hayley Camilleri, Helene M. 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Kadam, Sabino Matarrese, Samuel Brieden, Santiago González-Gaitán, Santosh V. Lohakare, Scott Watson, Shao-Jiang Wang, Simão Marques Nunes, Soumya Chakrabarti, Subinoy Das, Suvodip Mukherjee, Tajron Jurić, Tessa Baker, Theodoros Nakas, Tiago Barreiro, Upala Mukhopadhyay, Veljko Vujčić, Violetta Sagun, Vladimir A. Srećković, Wangzheng Zhang, Yo Toda, Yun-Song Piao, Zahra Davari

Physics of the Dark Universe, Volume: 49, Start page: 101965

Swansea University Author: Ivonne Zavala Carrasco Orcid Logo

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DOI (Published version): 10.1016/j.dark.2025.101965

Abstract

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by...

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Published in: Physics of the Dark Universe
ISSN: 2212-6864
Published: Elsevier BV 2025
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa70101
Abstract: The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold dark matter contribution, as well as very early-time inflationary physics, and underpinned by gravitation through general relativity. There have always been open questions about the soundness of the foundations of the standard model. However, recent years have shown that there may also be questions from the observational sector with the emergence of differences between certain cosmological probes. In this White Paper, we identify the key objectives that need to be addressed over the coming decade together with the core science projects that aim to meet these challenges. These discordances primarily rest on the divergence in the measurement of core cosmological parameters with varying levels of statistical confidence. These possible statistical tensions may be partially accounted for by systematics in various measurements or cosmological probes but there is also a growing indication of potential new physics beyond the standard model. After reviewing the principal probes used in the measurement of cosmological parameters, as well as potential systematics, we discuss the most promising array of potential new physics that may be observable in upcoming surveys. We also discuss the growing set of novel data analysis approaches that go beyond traditional methods to test physical models. These new methods will become increasingly important in the coming years as the volume of survey data continues to increase, and as the degeneracy between predictions of different physical models grows. There are several perspectives on the divergences between the values of cosmological parameters, such as the model-independent probes in the late Universe and model-dependent measurements in the early Universe, which we cover at length. The White Paper closes with a number of recommendations for the community to focus on for the upcoming decade of observational cosmology, statistical data analysis, and fundamental physics developments.
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College: Faculty of Science and Engineering
Funders: This paper is based upon work from COST Action CA21136 Addressing observational tensions in cosmology with systematics and fundamental physics (CosmoVerse) supported by COST (European Cooperation in Science and Technology). EDV is supported by a Royal Society Dorothy Hodgkin Research Fellowship. JLS would also like to acknowledge funding from “Xjenza Malta” as part of the “Technology Development Programme” DTP-2024-014 (CosmicLearning) Project and the “XM-TÜBÄ°TAK R&I Programme” BridgingCosmology project. AGV is funded by “la Caixa” Foundation, Spain (ID 100010434) and the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 847648, with fellowship code LCF/BQ/PI23/11970027. AP acknowledges support from the Polish National Science Centre through the grant 2023/50/A/ST9/00579. AP is supported by National Science Foundation Grant No. 2308193. CvdB is supported by the Lancaster–Sheffield Consortium for Fundamental Physics under STFC grant: ST/X000621/1. CU was supported by UKRI STFC ST/W001020 /1 and European Union ERC StG, LSS_BeyondAverage, 101075919. DE acknowledges support from the Swiss National Science Foundation (SNSF), Switzerland under grant agreement 200021_212576. EMT is supported by funding from the European Research Council (ERC) under the European Union’s HORIZON-ERC-2022 (grant agreement no. 101076865). ENS acknowledges the contribution of the LISA CosWG. This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement 853291). FB acknowledges the support of the Royal Society through the University Research Fellowship. The work of FN is supported by VR Starting Grant 2022-03160 of the Swedish Research Council. GB is supported by the Spanish grants CIPROM/2021/054 (Generalitat Valenciana) and PID2023-151418NB-I00 funded by MCIU/AEI/10.13039/501100011033. IS acknowledges NASA, United States grants N4-ADAP24-0021 and 24-ADAP24-0074, and this research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP). JT is supported by a Ramón Cajal contract by the Spanish Ministry for Science, Innovation and Universities with Ref. RYC2023-045660-I. JM would also like to acknowledge funding from “Xjenza Malta” as part of the “Technology Development Programme” DTP-2024-014 (CosmicLearning) Project. KS acknowledges support from the Australian Government through the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), through project number CE230100016. K.F.D. was supported by the PNRR-III-C9-2022–I9 call, with project number 760016/27.01.2023, and funding from “Xjenza Malta” as part of the “XM-TÜBÄ°TAK R&I Programme” BridgingCosmology project. LZ is supported by the NAWA Ulam fellowship (No. BPN/ULM/2023/1/00107/U/00001) and the National Science Centre, Poland (research grant No. 2021/42/E/ST2/ 00031). LG acknowledges financial support from AGAUR, CSIC, MCIN and AEI 10.13039/50110 0011033 under projects PID2023-151307NB-I00, PIE 20215AT016, CEX2020-001058-M, ILINK23001, COOPB2304, and 2021-SGR-01270. LV acknowledges support by the National Natural Science Foundation of China (NSFC) through the grant No. 123506 10240 “Astrophysical Axion Laboratories”, and also thanks INFN through the “QGSKY” Iniziativa Specifica project. The work of LAA is supported by the US National Science Foundation Grant PHY-2412679. MA acknowledges the UK Science and Technology Facilities Council (STFC) under grant number ST/Y002652/1 and the Royal Society, United Kingdom under grant numbers RGSR2222268 and ICAR1231094. MG acknowledges support from the European Union (ERC, RELiCS, project number 101116027) and the PRIN (Progetti di ricerca di Rilevante Interesse Nazionale) number 2022WJ9J33. MF is funded by the PRIN (Progetti di ricerca di Rilevante Interesse Nazionale) number 2022WJ9J33. MC, GR, and RH acknowledge support from the project “INAF-EDGE” (Large Grant 12-2022, P.I. L. Hunt), from the ASI-INAF agreement “Scientific Activity for the Euclid Mission” (n.2024-10-HH.0; WP8420) and from the INAF “Astrofisica Fondamentale” GO-grant 2024 (PI M. Cantiello). MM acknowledges support from MIUR, PRIN 2022 (grant 2022NY2ZRS 001) and from the grant ASI n. 2024-10-HH.0 “Attività scientifiche per la missione Euclid – fase E”. RCN thanks the financial support from the CNPq under the project No. 304306/2022-3 and FAPERGS under the project No. 23/2551-0000848-3. RCB is supported by an appointment to the JRG Program at the APCTP through the Science and Technology Promotion Fund and Lottery Fund of the Korean Government, and was also supported by the Korean Local Governments in Gyeongsangbuk-do Province and Pohang City. RC acknowledges support from the CONAHCYT research grant CF2022-320152. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 947660). RIA is funded by the SNSF Eccellenza Professorial Fellowship PCEFP2_194638. SK acknowledges funding by the National Center for Science, Poland, grant no. 2023/49/B/ST9/02777. SL is supported by the National Science Foundation Graduate Research Fellowship Program under grant No. DGE2139757. SV acknowledges support from the Istituto Nazionale di Fisica Nucleare (INFN) through the Commissione Scientifica Nazionale 4 (CSN4) Iniziativa Specifica “Quantum Fields in Gravity, Cosmology and Black Holes” (FLAG), and from the University of Trento and the Provincia Autonoma di Trento (PAT, Autonomous Province of Trento) through the UniTrento Internal Call for Research 2023 grant “Searching for Dark Energy off the beaten track” (DARKTRACK, grant agreement no. E63C22000500003). SP acknowledges the financial support from the Department of Science and Technology, Philippines (DST), Govt. of India under the Scheme “Fund for Improvement of S&T Infrastructure (FIST)” (File No. SR/FST/MS-I/2019/41). TT acknowledges support from the National Science Foundation, United States, the National Areonautics and Space Administration, and the Gordon and Betty Moore Foundation, United States. VP is supported by funding from the European Research Council (ERC) under the European Union’s HORIZON-ERC-2022 (grant agreement no. 101076865) and from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 860881-HIDDeN. AD acknowledges the support of the European Union’s Horizon 2021 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 101068013 (QGRANT). AK has been supported by a Lendület excellence grant by the Hungarian Academy of Sciences (MTA). This project has received funding from the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie grant agreement number 101130774. Funding for this project was also available in part through the Hungarian Ministry of Innovation and Technology NRDI Office grant OTKA NN147550. ARL was supported by FCT through the Investigador FCT Contract CEECIND/02854/2017 and the research project PTDC/FIS-AST/0054/2021. AP is grateful for the support of Vicerrectoría de Investigación Desarrollo Tecnológico (Vridt) at Universidad Católica del Norte through Núcleo de Investigación Geometría Diferencial Aplicaciones, Resolución Vridt No - 096/2022 and Resolución Vridt No - 098/2022. AP was supported by the Proyecto Fondecyt Regular 2024, Folio 1240514, Etapa 2024. AB acknowledges support from the National Science Center, project no. UMO-2022/45/B/ST2/01067. ABR is supported by the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), Grant No E-26/200.149/2025 é 200.150/2025 (304809) AJS received support from NASA, United States through STScI grants HST-GO-16773 and JWST-GO-2974. AM acknowledges the financial support by Conacyt-Mexico through the Post- doc Project I1200/311/2023. AB acknowledges the fellowship of the Brazilian research agency CNPq. AH is funded by the Carlsberg foundation. BSS acknowledges National Science Foundation awards AST-2307147, PHY-2207638, PHY-2308886 and PHY-2309064. B. L. acknowledges the support of the National Research Foundation of Korea, South Korea (NRF-2022R1F1A1076338), the Partenariat Hubert Curien STAR with the National Research Foundation of Korea (RS-2023-00259422), and of the Korea Institute for Advanced Study (KIAS) grant funded by the government of Korea. The research activities of BT is supported in part by the U.S. National Science Foundation under Grant PHY-2014104. CGB is supported by the Spanish Grant PID2023-149016NB-I00 (MINECO/AEI/FEDER, UE) and the Basque government Grant No. IT1628-22 (Spain). CM is supported by an FCT fellowship, grant number 2023.03984. CZ is supported by the China Scholarship Council for 1 year study at SISSA. CP acknowledges the financial support by the excellence cluster QuantumFrontiers of the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) under Germany’s Excellence Strategy – EXC-2123 QuantumFrontiers – 390837967 and was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Germany - Project Number 420243324. D.B. acknowledges support from projects PID2021-122938NB-I00 funded by the Spanish “Ministerio de Ciencia e Innovación” and FEDER “A way of making Europe”, PID2022-139841NB-I00 funded by the Spanish “Ministerio de Ciencia e Innovación” and SA097P24 funded by Junta de Castilla León. DS acknowledges support from Bulgarian National Science Fund, Republic of Bulgaria grant number KP-06-N58/5. DRG acknowledges support from grant PID2022-138607NBI00, funded by MCIN/AEI/10.13039/501100011033. DB acknowledges funding from the Ministry of Science, Technological Development and Innovations of the Republic of Serbia, Project contract No. 451-03-136/2025-03/200017. The work of EG was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP). EF is supported by “Theoretical Astroparticle Physics” (TAsP), iniziativa specifica INFN and by the research grant number 2022E2J4RK “PANTHEON: Perspectives in Astroparticle and Neutrino THEory with Old and New messengers”under the program PRIN 2022 funded by the Italian Ministero dell’Università e della Ricerca (MUR). EDMF is supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. FA thanks CNPq and Fundação Carlos Chagas Filho de Amparo á Pesquisa do Estado do Rio de Janeiro (FAPERJ), Processo SEI 260003/014913/2023 for financial support. The work of FB was supported by the postdoctoral grant CIAPOS/2021/169. FP acknowledges partial support from the INFN grant InDark and from the Italian Ministry of University and Research (mur), PRIN 2022 ‘EXSKALIBUR – Euclid-Cross-SKA: Likelihood Inference Building for Universe’s Research’, Grant No. 20222BBYB9, CUP C53D2300131 0006, and from the European Union – Next Generation EU. FP also acknowledges support from the FCT project “BEYLA – BEYond LAmbda” with ref. number PTDC/FIS-AST/0054/2021. FSNL acknowledges support from the Fundação para a Ciência e a Tecnologia (FCT) Scientific Employment Stimulus contract with reference CEECINST/00032/2018, and funding through the research grants UIDB/04434/2020, UIDP/04434/2020 and PTDC/FIS-AST/0054/2021. GL was funded by Agencia Nacional de Investigación Desarrollo (ANID) through Proyecto Fondecyt Regular 2024, Folio 1240514, Etapa 2024. He also thanks Vicerrectorá de Investigación Desarrollo Tecnológico (VRIDT) at Universidad Católica del Norte for support through Núcleo de Investigación Geometría Diferencial Aplicaciones (Resolución VRIDT N°096/2022). GG acknowledges the financial support from the COSMOS network (www.cosmosnet.it) through the ASI (Italian Space Agency) Grants 2016-24-H.0 and 2016-24-H.1- 2018. GDS acknowledges support from INAF-ASTROFIT fellowship and Istituto Nazionale di Fisica Nucleare (INFN), Naples Section, for specific initiatives QGSKY and Moonlight2, as well as GAIA DPAC funds from INAF and ASI (PI: M.Lattanzi). GJO acknowledges financial support from the Spanish Grants PID2020-116567GB-C21, PID2023-149560NB-C21 funded by MCIN/AEI/10.13039/501100011033, by CEX2023-001292-S funded by MCIU/AEI, and by i-COOP23096 funded by CSIC. GSDj acknowledges the support by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia under contract 451-03-137/2025-03/ 200124 and support by the ICTP - SEENET-MTP NT03 Project TECOM-GRASP. GCH acknowledges support through the ESA research fellowship programm. HAF was partially supported by National Science Foundation grant AST-1907404. The work of IDG was supported by the Estonian Research Council, Estonia grants MOB3JD1202, RVTT3, RVTT7, and by the CoE program TK202 “Fundamental Universe”. The work of IAM is supported by the Basque Government, Spain Grant IT1628-22, by Grant PID2021-123226NB-I00 (funded by MCIN/AEI/10.13039/5011000 11033 and by “ERDF A way of making Europe”). IDM acknowledges support from the grant PID2021-122938NB-I00 funded by MCIN/AEI/ 10.130 39/501100011033 and from the grant SA097P24 funded by Junta de Castilla León and by “ERDF A way of making Europe”. JA acknowledges support from the Diputación General de Aragón-Fondo Social Europeo (DGA-FSE) Grant No. 2020-E21-17R of the Aragon Government. JG and BK have been supported in part by the Polish National Science Center (NCN) under grant 2020/37/B/ST2/02371. JR is supported by a Ramón Cajal contract of the Spanish Ministry of Science and Innovation with Ref. RYC2020-028870-I. This research was further supported by the project PID2022-139841NB-I00 of MICIU/AEI/10.13039/501100011033 and FEDER, UE. JS is supported by the Taiwan National Science & Technology Council. JARC is supported by the project PID2022-139841NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by ERDF/EU. JJ acknowledge partial support from STScI, United States under grants HST-GO-16262 and JWST-GO-03055. JGB acknowledges support from the Spanish Research Project PID2021-123012NB-C43 [MICINN-FEDER], and the Centro de Excelencia Severo Ochoa Program, Spain CEX2020-001007-S at IFT. KL is a recipient of the John and Pat Hume Scholarship and acknowledges support from the Friedrich Naumann Foundation for Freedom and from the Swiss Study Foundation. The research activities of KRD are supported in part by the U.S. National Science Foundation through its employee IR/D program as well as by the U.S. Department of Energy under Grant DE-FG02-13ER41976/DE-SC0009913. LLG acknowledges support from Conselho Nacional de Desenvolvimento Cientıfico e Tecnologico (CNPq), Grant No. 307636/2023-2 and from the Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro (FAPERJ) Grant No. E-26/204.598/2024. LY acknowledges support from YST Program of APCTP and Natural Science Foundation of Shanghai 24ZR1424600. LC acknowledges support from FCT - Fundação para a Ciência e a Tecnologia through the projects with DOI identifiers 10.54499/2023.11681.PEX and 10.54499/2024.00249.CERN. MB is supported by the Polish National Science Center through grants no. 2020/38/E/ST9/00395 and 2020/39/B/ST9/03494. MGE acknowledges the financial support of FONDECYT de Postdoctorado, N°3230801. MdC acknowledges support from INFN iniziativa specifica GeoSymQFT. The work of MR is supported by the European Union – Next Generation EU and by the Italian Ministry of University and Research (MUR) via the PRIN 2022 project n. 20228WHTYC. ME was supported by the Estonian Ministry of Education and Research (grant TK202, “Foundations of the Universe”), by Estonian Research Council, Estonia grant PRG2172, and by the European Union’s Horizon Europe research and innovation programme (EXCOSM, grant No. 101159513). The work of MBL, CGB & PM is supported by the Spanish Grant PID2023-149016NB-I00 (MINECO/AEI/FEDER, UE). This work is also supported by the Basque government Grant No. IT1628-22 (Spain). MC was supported by FCT through the Investigador FCT Contract No. CEECIND/02581/2018 and the research project PTDC/FIS-AST/0054/ 2021. MM acknowledges funding by the Agenzia Spaziale Italiana, Italy (asi) under agreement no. 2018-23-HH.0 and support from INFN/Euclid Sezione di Roma. MASP acknowledges support from the FCT through the Fellowship UI/BD/154479/2022, through the Research Grants UIDB/04434/ 2020 and UIDP/04434/2020, and through the project with reference PTDC/FIS-AST/0054/2021 (“BEYond LAmbda”). MASP also acknowledges support from the MICINU through the project with reference PID2023-149560NB-C21. MAS received support from the CAPES scholarship. MK was funded through SASPRO2 project AGE of Gravity: Alternative Geometries of Gravity, which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 945478. MM acknowledges the support by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia under contract 451-03-137/2025-03/ 200124. MI acknowledges that this material is based upon work supported in part by the Department of Energy, Office of Science, under Award Number DE-SC0022184 and also in part by the U.S. National Science Foundation under grant AST2327245. NF acknowledge support from the Research grant TAsP (Theoretical Astroparticle Physics) funded by INFN, Italy. NF is supported by the European Union – Next Generation EU and by the Italian Ministry of University and Research (MUR) via the PRIN 2022 project n. 20228WHTYC. The Work of NEM. is supported in part by the UK Science and Technology Facilities research Council (STFC) under the research grant ST/X000753/1. NAN was financed by IBS, United States under the project code IBS-R018-D3, and acknowledges support from PSL/Observatoire de Paris. NS is supported by the Charles University Grant Agency (GAUK) - 94224. PS is supported by Science and Technology Facilities Council, United Kingdom (STFC) training grant ST/X508287/1. PJ acknowledges funding from the Ministry of Science, Technological Development and Innovations of the Republic of Serbia, Project contract No. 451-03-136/2025-03/200002. RG acknowledges the support from the SNF 200020_175751 and 200020_207379 “Cosmology with 3D Maps of the Universe” research grant. RH work has been supported by the Spanish grants FPU19/03348 of MU, MCIN/AEI/10.13039/501100011033 grants PID2020-113644GB-I00, PID2023-148162NB-C22, by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grants HORIZON-MSCA-2021-SE-01/ 101086085-ASYMMETRY and H2020-MSCA-ITN-2019/ 860881- HIDDeN and by the Generalitat Valenciana grants PROMETEO/2019/ 083 and CIPROM/2022/69. RH acknowledges funding from the Italian National Institute of Astrophysics (INAF) through large grant PRIN 12-2022 “INAF-EDGE” (PI L. Hunt). RR acknowledges financial support from the STFC Consolidated Grant ST/X000583/1. RBN acknowledges funding by the Royal Society, United Kingdom through the University Research Fellowship Renewal URF R 221005. RK is supported by Project SA097P24 funded by Junta de Castilla Leon. SB is supported by “Agencia Nacional de Investigación Desarrollo” (ANID), Grant “Becas Chile postdoctorado al extranjero” No. 74220006. ST is supported by the National Science Centre, Poland (research grant No. 2021/42/E/ST2/00031). SSC acknowledges support from the Istituto Nazionale di Fisica Nucleare (INFN) through the Commissione Scientifica Nazionale 4 (CSN4) Iniziativa Specifica “Quantum Fields in Gravity, Cosmology and Black Holes” (FLAG) and from the Fondazione Cassa di Risparmio di Trento e Rovereto (CARITRO Foundation) through a Caritro Fellowship (project “Inflation and dark sector physics in light of next-generation cosmological surveys”). SJL is supported by grant PIP 11220200100729CO CONICET and grant 20020170100129BA UBACYT. SP is supported by the international Gemini Observatory, a program of NSF NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the U.S. National Science Foundation, on behalf of the Gemini partnership of Argentina, Brazil, Canada, Chile, the Republic of Korea, and the United States of America. SP acknowledges the financial support of the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fellowships 300936/2023-0 and 301628/2024-6. TP acknowledges the financial support from the Slovenian Research Agency (grants I0-0033, P1-0031, J1-8136, J1-2460 and Z1-1853). TB was supported by ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, funded by European Union – NextGenerationEU. TS is supported by the Della Riccia foundation grant 2025 and the Galileo Galilei Institute Boost Fellowship 2024. TK was supported by the Estonian Research Council, Estonia grants CoE TK202 “Foundations of the Universe” and PRG2608 “Space - Time - Matter”. VM thanks CNPq (Brazil) and FAPES (Brazil) for partial financial support. VAM is supported by Generalitat Valenciana via the Excellence Grant 164CIPROM/2021/073, by the Spanish MICIN/AEI/10.13039/501100011033 and the EU/FEDER via grant PID2021-122134NB-C21, and by the Spanish MCIU/AEI via the Severo Ochoa project CEX2023-001292-S. VP acknowledges the support by the Ministry of Education and Science of the Federation of Bosnia and Herzegovina, under Project Number 05-35-2467-1/23. VK acknowledges financial support from Research Ireland Grant 21/PATH-S/9475 (MOREHIGGS) under the SFI-IRC Pathway Programme. Report number: DIAS-STP-25-05. VM acknowledges support from ANID FONDECYT Regular grant number 1231418, Millennium Science Initiative AIM23-0001, and Centro de Astrofísica de Valparaíso CIDI N21. VBJ acknowledges funding from the Ministry of Science, Technological Development and Innovations of the Republic of Serbia, Project contract No. 451-03-136/2025-03/200017. WY has been supported by the National Natural Science Foundation of China under Grant No. 12175096, and Liaoning Revitalization Talents Program under Grant no. XLYC1907098. WY is supported via the research projects ‘COLAB’ funded by the National Science Center, Poland, under agreement number UMO-2020/39/B/ST9/03494. “YH is funded by NSFC under the grant No. 12347137 and the China Postdoctoral Science Foundation, China under Grant No. 2024M753076”.
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