arXiv subjects
Publications and source records attributed to John Miritzis.
We study the closed universe recollapse conjecture for positively curved Friedmann-Robertson-Walker (FRW) models in the Jordan frame of the second order gravity theory. We analyse the late time evolution of the model with the methods of the dynamical systems. We find that an initially expanding closed FRW universe, starting close to the Minkowski spacetime, may exhibit oscillatory behaviour.
We study the closed universe recollapse conjecture for positively curved FRW models with a perfect fluid matter source and a scalar field which arises in the conformal frame of the $R+αR^{2}$ theory. By including ordinary matter, we extend the analysis of a previous work. We analyze the structure of the resulted four-dimensional dynamical system with the methods of the center manifold theory and the normal form theory. It is shown that an initially expanding closed FRW universe, starting close to the Minkowski spacetime, cannot avoid recollapse. We discuss the posibility that potentials with a positive minimum may prevent the recollapse of closed universes.
We study homogeneous and isotropic cosmologies in a Weyl spacetime. We show that for homogeneous and isotropic spacetimes, the field equations can be reduced to the Einstein equations with a two-fluid source. We write the equations as a two-dimensional dynamical system and analyze the qualitative, asymptotic behavior of the models. We examine the possibility that in certain theories the Weyl 1-form may give rise to a late accelerated expansion of the Universe and conclude that such behaviour is not met as a generic feature of the simplest cosmologies.
We study the late time evolution of positively curved FRW models with a scalar field which arises in the conformal frame of the $R+αR^{2}$ theory. The resulted three-dimensional dynamical system has two equilibrium solutions corresponding to a de Sitter space and an ever expanding closed universe. We analyze the structure of the first equilibrium with the methods of the center manifold theory and, for the second equilibrium we apply the normal form theory to obtain a simplified system, which we analyze with special phase plane methods. It is shown that an initially expanding closed FRW spacetime avoids recollapse.
We study the late time evolution of flat and negatively curved FRW models with a perfect fluid matter source and a scalar field having an arbitrary non-negative potential function $V(ϕ) .$ We prove using a dynamical systems approach four general results for a large class of non-negative potentials which show that almost always the universe ever expands. In particular, for potentials having a local zero minimum, flat and negatively curved FRW models are ever expanding and the energy density asymptotically approaches zero. We investigate the conditions under which the scalar field asymptotically approaches the minimum of the potential. We discuss the question of whether a closed FRW with ordinary matter can avoid recollapse due to the presence of a scalar field with a non-negative potential.
We examine theories of gravity which include finitely many coupled scalar fields with arbitrary couplings to the curvature (wavemaps). We show that the most general scalar-tensor $σ$-model action is conformally equivalent to general relativity with a minimally coupled wavemap with a particular target metric. Inflation on the source manifold is then shown to occur in a novel way due to the combined effect of arbitrary curvature couplings and wavemap self-interactions. A new interpretation of the conformal equivalence theorem proved for such `wavemap-tensor' theories through brane-bulk dynamics is also discussed.
This paper considers some physically interesting cosmological dynamical systems in the FRW-scalarfield category which are examined for integrability according to the criterion of Painlevé. In the literature these systems have been examined from the point of view of dynamical systems and the results from the two disparate methods of analysis are compared. This allows some more general comments to be made on the use of the Painlevé method in covariant systems.
We show that the scalar-tensor $σ$-model action is conformally equivalent to general relativity with a minimally coupled wavemap with a particular target metric. Inflation on the source manifold is then shown to occur in a natural way due both to the arbitrary curvature couplings and the wavemap self-interactions.
For dynamical systems of dimension three or more the question of integrability or nonintegrability is extended by the possibility of chaotic behaviour in the general solution. We determine the integrability of isotropic cosmological models in general relativity and string theory with a variety of matter terms, by a performance of the Painlevé analysis in an effort to examine whether or not there exists a Laurent expansion of the solution about a movable pole which contains the number of arbitrary constants necessary for a general solution.
We apply the results of singularity analysis to the isotropic cosmological models in general relativity and string theory with a variety of matter terms. For some of these models the standard Painlevé test is sufficient to demonstrate integrability or nonintegrability in the sense of Painlevé. For others of these models it is necessary to use a less algorithmic procedure.