Comptes Rendus
no. 6-7
Everything you always wanted to know about the cosmological constant problem (but were afraid to ask)
[Tout ce que vous avez toujours voulu savoir sur le problème de la constante cosmologique sans jamais avoir osé le demander]
Jérôme Martin1
1 Institut dʼastrophysique de Paris, UMR7095-CNRS, université Pierre-et-Marie-Curie, 98 bis, boulevard Arago, 75014 Paris, France
Comptes Rendus. Physique, Volume 13 (2012) no. 6-7, pp. 566-665.

Cet article traite du problème de la constante cosmologique dʼune manière pédagogique aussi bien que technique. Nous passons en revue comment lʼénergie du vide peut être régularisée en espace temps plat et courbe, et comment son calcul peut être compris en termes de diagrammes de Feynman en bulles. En particulier, nous montrons que la valeur correctement renormalisée de lʼénergie de point zéro maintenant (pour une théorie libre) en en fait bien au dessous des 122 ordres de grandeur de lʼénergie critique de lʼunivers. Nous nous concentrons sur le cas des champs scalaires bien que nous considérions le cas des fermions et des bosons de jauge également afin de traiter lʼénergie du vide en supersymétrie. Nous discutons aussi comment la constante cosmologique peut être mesurée cosmologiquement et contrainte par la mesure de lʼorbite des planètes du système solaire ou encore des spectres atomiques. Nous passons aussi en revue pourquoi la mesure du Lamb shift et de lʼeffet Casimir semblent indiquer que les fluctuations quantiques de lʼénergie du vide ne sont pas un artefact du formalisme de la théorie des champs. Nous montrons ensuite comment les expériences sur lʼuniversalité de la chute libre peuvent aider à contraindre les propriétés gravitationnelles de lʼénergie du vide et nous discutons le statut du principe dʼéquivalence faible en mécanique quantique, en particulier lʼexpérience de Colella, Overhauser et Werner ainsi que lʼexpérience de Galilée quantique faite avec une horloge de Salecker–Wigner–Peres. Enfin, nous concluons brièvement avec une discussion sur les différentes solutions au problème de la constante cosmologique qui ont été proposées jusquʼà présent.

This article aims at discussing the cosmological constant problem at a pedagogical but fully technical level. We review how the vacuum energy can be regularized in flat and curved space–time and how it can be understood in terms of Feynman bubble diagrams. In particular, we show that the properly renormalized value of the zero-point energy density today (for a free theory) is in fact far from being 122 orders of magnitude larger than the critical energy density, as often quoted in the literature. We mainly consider the case of scalar fields but also treat the cases of fermions and gauge bosons which allows us to discuss the question of vacuum energy in super-symmetry. Then, we discuss how the cosmological constant can be measured in cosmology and constrained with experiments such as measurements of planet orbits in our solar system or atomic spectra. We also review why the Lamb shift and the Casimir effect seem to indicate that the quantum zero-point fluctuations are not an artifact of the quantum field theory formalism. We investigate how experiments on the universality of free fall can constrain the gravitational properties of vacuum energy and we discuss the status of the weak equivalence principle in quantum mechanics, in particular the Colella, Overhauser and Werner experiment and the quantum Galileo experiment performed with a Salecker–Wigner–Peres clock. Finally, we briefly conclude with a discussion on the solutions to the cosmological constant problem that have been proposed so far.

Publié le :
DOI : 10.1016/j.crhy.2012.04.008
Keywords: Cosmological constant problem, Feynman bubble diagrams, Super-symmetry, Vacuum energy
Mot clés : Problème de la constante cosmologique, Diagrammes de Feynman en bulles, Supersymétrie, Énergie du vide
Jérôme Martin 1

1 Institut dʼastrophysique de Paris, UMR7095-CNRS, université Pierre-et-Marie-Curie, 98 bis, boulevard Arago, 75014 Paris, France 
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Jérôme Martin. Everything you always wanted to know about the cosmological constant problem (but were afraid to ask). Comptes Rendus. Physique, Volume 13 (2012) no. 6-7, pp. 566-665. doi : 10.1016/j.crhy.2012.04.008. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2012.04.008/

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