Jaime A. Stein-Schabes

The Critical Dimension for Chaotic Cosmology

Abstract Using the ADM formalism for general relativity the approach to a space-time singularity of a general inhomogeneous universe, in an arbitrary number of dimensions, is studied. The question of whether chaotic behaviour is a generic feature of Einsteins equations, in an arbitrary number of dimensions, is explored. We find that models that contain ten or more spatial dimensions are non-chaotic and their approach toward the initial singularity is monotonic, whereas for those with dimensionality between four and nine their approach is chaotic. A clear geometrical picture is constructed whereby this result can be understood.

A no-hair theorem for R2 models

Abstract We show that the R + ϵR 2 theory for homogeneous spacetimes, satisfies all the energy conditions required by the NHT and so it inflates. As the universe approaches this phase it has already become sufficiently flat and isotropic, leaving the production of density perturbations to the de Sitter phase. When there is an explicit λ term i.e. R + ϵR 2 −2 λ the model naturally leads into double inflation, where the R 2 inflationary phase is followed by the ϵ driven phase. We investigate the constraints on the initial conditions due to the finite duration of the R 2 inflation and find that all but a small fraction of the available phase space leads to sufficient inflation.

Inflation in anisotropic scalar-tensor theories

Abstract The existence of an inflationary phase in anisotropic scalar-tensor theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a a non-trivial potential. We then use the explicit form of the potential and the no hair theorem to conclude that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.

A No-hair Theorem for Inhomogeneous Cosmologies

We show that under very general conditions any inhomogeneous cosmological model with a positive cosmological constant, that can be described in a synchronous reference system will tend asymptotically in time towards the de Sitter solution, so making the problem of initial conditions less severe. The implications for inflationary scenarios are examined and it is found that after inflation the universe stays isotropic and homogeneous for a very long time.

Cosmic strings in an expanding spacetime

We investigate the stability of a static, infinitely long and straight vacuum string solution under inhomogeneous axisymmetric time-dependent perturbations. We find it to be perturbatively stable. We further extend our work by finding a string solutions in an expanding Universe. The back reaction of the string on the gravitational field has been ignored. The background is assumed to be a Friedman-Robertson-Walker (FRW) cosmology. By numerically integrating the field equations in a radiation and matter dominated models, we discover oscillatory solutions. The possible damping of these oscillations is discussed. For late times the solution becomes identical to the static one studied in the first part of the paper. 19 refs., 8 figs.