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Comptes Rendus Physique
Volume 18, n° 3-4
pages 265-274 (mars 2017)
Doi : 10.1016/j.crhy.2017.04.002
CDT and cosmology
Les triangulations dynamiques causales et la cosmologie

Lisa Glaser , Renate Loll
 Radboud University, Institute for Mathematics, Astrophysics and Particle Physics, Heyendaalseweg 135, NL-6525 AJ Nijmegen, The Netherlands 

Corresponding authors.

In the approach of Causal Dynamical Triangulations (CDT), quantum gravity is obtained as a scaling limit of a non-perturbative path integral over space-times whose causal structure plays a crucial role in the construction. After some general considerations about the relation between quantum gravity and cosmology, we examine which aspects of CDT are potentially interesting from a cosmological point of view, focusing on the emergence of a de Sitter universe in CDT quantum gravity.

The full text of this article is available in PDF format.

Dans l'approche des triangulations dynamiques causales (CDT), la gravitation quantique est obtenue comme une limite d'échelle d'une intégrale de chemin non perturbative sur des espaces-temps dont la structure causale joue un rôle crucial dans la construction. Après quelques considérations générales sur la relation entre la gravité quantique et la cosmologie, nous examinons quels aspects des triangulations dynamiques causales sont potentiellement intéressants d'un point de vue cosmologique, en mettant l'accent sur l'émergence d'un univers de de Sitter en gravitation quantique dans l'approche CDT.

The full text of this article is available in PDF format.

Keywords : Causal dynamic triangulation, Quantum gravity, Cosmology

Mots-clés : Triangulation dynamique causale, Gravitation quantique, Cosmologie

1  Nor would it in general be possible to introduce coordinates in neighbourhoods that extend beyond individual building blocks, because of the presence of curvature singularities.
2  In all space-time dimensions studied so far: two, three and four.
3  Note that after a Wick rotation  , Lorentzian de Sitter space becomes Euclidean de Sitter space, which geometrically is a round four-sphere.
4  One reason why the dimension does not have to be 4, despite the use of four-dimensional building blocks, is that we perform a nontrivial continuum limit in which specific properties present at the cutoff scale need not survive.
5  The lattice spacing a , introduced earlier as the length of an edge of a simplex, should not be confused with the Friedmann scale factor   used elsewhere in the text. Note that all CDT results quoted are obtained through finite-size scaling in the limit as   or, equivalently, as the UV-cutoff  .
6  Fig. 5 is simply a curve made into a body of revolution.
7  Note that we are comparing the actions at fixed four-volume, where Λ is a Lagrange multiplier, in order to match the situation present in the Monte Carlo simulations.

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