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Our knowledge about the universe has increased tremendously in the last three decades or so --- thanks to the progress in observations --- but our understanding has improved very little. There are several fundamental questions about our universe for which we have no answers within the current, operationally very successful, approach to cosmology. Worse still, we do not even know how to address some of these issues within the conventional approach to cosmology. This fact suggests that we are missing some important theoretical ingredients in the overall description of the cosmos. I will argue that these issues --- some of which are not fully appreciated or emphasized in the literature --- demand a paradigm shift: We should not think of the universe as described by a specific solution to the gravitational field equations; instead, it should be treated as a special physical system governed by a different mathematical description, rooted in the quantum description of spacetime. I will outline how this can possibly be done., Comment: Invited Review; 28 pages; 1 figure

We review recent progress in numerical relativity simulations of black-hole (BH) spacetimes. Following a brief summary of the methods employed in the modeling, we summarize the key results in three major areas of BH physics: (i) BHs as sources of gravitational waves (GWs), (ii) astrophysical systems involving BHs, and (iii) BHs in high-energy physics. We conclude with a list of the most urgent tasks for numerical relativity in these three areas., Comment: Updated version, references added; 47 pages, 3 figures

Assuming the universe is spatially homogeneous on the largest scales lays the foundation for almost all cosmology. This idea is based on the Copernican principle, that we are not at a particularly special place in the universe. Surprisingly, this philosophical assumption has yet to be rigorously demonstrated independently of the standard paradigm. This issue has been brought to light by cosmological models which can potentially explain apparent acceleration by spatial inhomogeneity rather than dark energy. These models replace the temporal fine tuning associated with Lambda with a spatial fine tuning, and so violate the Copernican assumption. While is seems unlikely that such models can really give a realistic solution to the dark energy problem, they do reveal how poorly constrained radial inhomogeneity actually is. So the bigger issue remains: How do we robustly test the Copernican principle independently of dark energy or theory of gravity?, Comment: 40 pages, 15 figures. Accepted review article to appear in a special volume of the "Comptes Rendus de l'Academie des Sciences" about Dark Energy and Dark Matter

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 Collela, Overhausser 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., 89 pages, 14 figures, Accepted review article to appear in a special volume of the "Comptes Rendus de l'Academie des Sciences" about Dark Energy and Dark Matter