Cosmology, the big bang and the BKL conjecture

Hans Ringström

doi:10.5802/crmeca.277

Article de synthèse

Cosmology, the big bang and the BKL conjecture
[Cosmologie, big bang et conjecture BKL]

Hans Ringström ¹

¹ Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden

Comptes Rendus. Mécanique, Volume 353 (2025), pp. 53-78.

Résumé
Abstract

Il s’agit d’un article de revue sur les résultats mathématiques en cosmologie, écrit en l’honneur du 100ème anniversaire d’Yvonne Choquet-Bruhat. Il commence par une brève description de certaines questions essentielles : la censure cosmique forte, la relation entre l’asymptotique future et la géométrisation dans le cas du vide, la conjecture de l’absence de cheveux dans le cadre cosmique et la proposition BKL. Il aborde ensuite les résultats, en commençant par ceux obtenus dans des situations avec symétrie. Il se poursuit par un examen des résultats de stabilité future non linéaire globale, des résultats de formation stable du big bang, des résultats concernant les solutions d’équations linéaires sur les espaces-temps cosmologiques et des résultats numériques. L’article contient une liste substantielle, mais très incomplète, de références à la littérature.

This is a review article of mathematical results in cosmology, written in honor of Yvonne Choquet-Bruhat’s 100th birthday. It starts with a brief description of some of the essential questions: strong cosmic censorship; the relation between the future asymptotics and geometrization in the vacuum setting; the cosmic no-hair conjecture; and the BKL-proposal. It then turns to results, starting with ones obtained in situations with symmetry. It continues with a review of future global non-linear stability results, stable big bang formation results, results concerning solutions to linear equations on cosmological backgrounds and numerical results. The article contains a substantial, but very incomplete, list of references to the literature.

Reçu le : 2024-10-11
Révisé le : 2024-12-02
Accepté le : 2024-12-03
Publié le : 2025-01-08

DOI : 10.5802/crmeca.277

Keywords: Global analysis, General relativity, Lorentzian geometry, Nonlinear evolution equations, Cosmology, The big bang and the BKL proposal
Mots-clés : Analyse globale, Relativité générale, Géométrie lorentzienne, Équations d’évolution non linéaires, Cosmologie, Big bang et proposition BKL

Affiliations des auteurs :

Hans Ringström ¹

¹ Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Hans Ringström. Cosmology, the big bang and the BKL conjecture. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 53-78. doi : 10.5802/crmeca.277. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.277/

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