Coupled quintessence and curvature-assisted acceleration

Spatially homogeneous models with a scalar field non-minimally coupled to the space-time curvature or to the ordinary matter content are analysed with respect to late-time asymptotic behaviour, in particular to accelerated expansion and isotropization. It is found that a direct coupling to the curvature leads to asymptotic de Sitter expansion in arbitrary exponential potentials, thus yielding a positive cosmological constant although none is apparent in the potential. This holds true regardless of the steepness of the potential or the smallness of the coupling constant. For matter-coupled scalar fields, the asymptotics are obtained for a large class of positive potentials, generalizing the well-known cosmic no-hair theorems for minimal coupling. In this case it is observed that the direct coupling to matter does not impact the late-time dynamics essentially.Comment: 17 pages, no figures. v2: typos correcte

Global existence and future asymptotic behaviour for solutions of the Einstein-Vlasov-scalar field system with surface symmetry

We prove in the cases of plane and hyperbolic symmetries a global in time existence result in the future for comological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a distribution function and a scalar field, subject to the Vlasov and wave equations respectively. The spacetime is future geodesically complete in the special case of plane symmetry with only a scalar field. Causal geodesics are also shown to be future complete for homogeneous solutions of the Einstein-Vlasov-scalar field system with plane and hyperbolic symmetry.Comment: 14 page

Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry

The late-time behaviour of the Einstein-dust system is well understood for homogeneous spacetimes. For the case of Bianchi I we have been able to show that the late-time behaviour of the Einstein-Vlasov system is well approximated by the Einstein-dust system assuming that one is close to the unique stationary solution which is the attractor of the Einstein-dust system.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010, to appear in Journal of Physics: Conference Series (JPCS

Inextendibility of expanding cosmological models with symmetry

A new criterion for inextendibility of expanding cosmological models with symmetry is presented. It is applied to derive a number of new results and to simplify the proofs of existing ones. In particular it shows that the solutions of the Einstein-Vlasov system with $T^2$ symmetry, including the vacuum solutions, are inextendible in the future. The technique introduced adds a qualitatively new element to the available tool-kit for studying strong cosmic censorship.Comment: 7 page

Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry

The late-time behaviour of the Einstein-dust system is well understood for homogeneous spacetimes. For the case of Bianchi I we have been able to show that the late-time behaviour of the Einstein-Vlasov system is well approximated by the Einstein-dust system assuming that one is close to the unique stationary solution which is the attractor of the Einstein-dust system.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010, to appear in Journal of Physics: Conference Series (JPCS

Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry

The late-time behaviour of the Einstein-dust system is well understood for homogeneous spacetimes. For the case of Bianchi I we have been able to show that the late-time behaviour of the Einstein-Vlasov system is well approximated by the Einstein-dust system assuming that one is close to the unique stationary solution which is the attractor of the Einstein-dust system.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010, to appear in Journal of Physics: Conference Series (JPCS

Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system

Using ODE techniques we prove the existence of large classes of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system. These include data for which the ratio of total charge to total mass is arbitrarily large.Comment: 12 page

Fuchsian methods and spacetime singularities

Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian equations have been recalled, various ways in which these equations have been applied in general relativity are described. Possible future applications are indicated

Late-time oscillatory behaviour for self-gravitating scalar fields

This paper investigates the late-time behaviour of certain cosmological models where oscillations play an essential role. Rigorous results are proved on the asymptotics of homogeneous and isotropic spacetimes with a linear massive scalar field as source. Various generalizations are obtained for nonlinear massive scalar fields, $k$-essence models and $f(R)$ gravity. The effect of adding ordinary matter is discussed as is the case of nonlinear scalar fields whose potential has a degenerate zero.Comment: 17 pages, additional reference

Local and global existence theorems for the Einstein equations

This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first. Next global results for solutions with symmetry are discussed. A selection of results from Newtonian theory and special relativity which offer useful comparisons is presented. This is followed by a survey of global results in the case of small data and results on constructing spacetimes with given singularity structure. The article ends with some miscellaneous topics connected with the main theme