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Advances in Astronomy
Volume 2012, Article ID 430694, 14 pages
Research Article

Fab Four: When John and George Play Gravitation and Cosmology

1Namur Center for Complex Systems (naXys), University of Namur, 5000 Namur, Belgium
2Faculté des Sciences et Techniques, Université d'Abomey-Calavi, BP 526 Cotonou, Benin
3Royal Observatory of Belgium, Avenue Circulaire 3, 1180 Brussels, Belgium
4LNE-SYRTE, Observatoire de Paris, CNRS, UPMC, avenue de l'Observatoire 61, 75014 Paris, France
5Center for Cosmology, Particle Physics and Phenomenology (CP3), University of Louvain, 1348 Louvain-la-Neuve, Belgium

Received 17 March 2012; Accepted 4 November 2012

Academic Editor: Elmetwally Elabbasy

Copyright © 2012 J.-P. Bruneton et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Scalar-tensor theories of gravitation attract again a great interest since the discovery of the Chameleon mechanism and of the Galileon models. The former allows reconciling the presence of a scalar field with the constraints from Solar System experiments. The latter leads to inflationary models that do not need ad hoc potentials. Further generalizations lead to a tensor-scalar theory, dubbed the “Fab Four,” with only first and second order derivatives of the fields in the equations of motion that self-tune to a vanishing cosmological constant. This model needs to be confronted with experimental data in order to constrain its large parameter space. We present some results regarding a subset of this theory named “John,” which corresponds to a nonminimal derivative coupling between the scalar field and the Einstein tensor in the action. We show that this coupling gives rise to an inflationary model with very unnatural initial conditions. Thus, we include the term named “George,” namely, a nonminimal, but nonderivative, coupling between the scalar field and Ricci scalar. We find a more natural inflationary model, and, by performing a post-Newtonian analysis, we derive the set of equations that constrain the parameter space with data from experiments in the Solar System.