相关论文: Global dynamics of cosmological scalar fields -- P…
We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois group approach, as introduced by Morales-Ruiz and Ramis. The…
We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois group approach, as introduced by Morales-Ruiz and Ramis. The…
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…
We construct integrable chiral cosmological models with two scalar fields and potentials represented in terms of hyperbolic functions. Using the conformal transformation of the metric and the corresponding models with induced gravity terms,…
In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and…
Recently a cubic Galileon cosmological model was derived by the assumption that the field equations are invariant under the action of point transformations. The cubic Galileon model admits a second conservation law which means that the…
We consider anisotropic cosmological models with an universe of dimension 4 or more, factorized into n>1 Ricci-flat spaces, containing an m-component perfect fluid of m non-interacting homogeneous minimally coupled scalar fields under…
We extend the investigation of cosmological dynamics of the general non-canonical scalar field models by dynamical system techniques for a broad class of potentials and coupling functions. In other words, we do not restrict the analysis to…
The strange behaviour of the universe's dark sector offers us the flexibility to address cosmological problems with different approaches. Using this flexibility, we consider a possible exchange of energy among the dark sector components as…
We study the integrable model with minimally and non-minimally coupled scalar fields and the correspondence of their general solutions. Using the model with a minimally coupled scalar field and a the constant potential as an example we…
We revisit the global dynamics of unified dark matter cosmological models and analyze it in a new dynamical system setting. In particular, by defining a suitable set of variables we obtain a bounded variable space, a feature that allows a…
Cosmological singularity and asymptotic behaviour of scale factor of generalized cosmological models are analyzed in respect of their structural stability. It is shown, that cosmological singularity is structurally unstable for the majority…
We study the Friedmann-Robertson-Walker model with phantom fields modelled in terms of scalar fields. We apply the Ziglin theory of integrability and find that the flat model is nonintegrable. Then we cannot expect to determine simple…
We consider multidimensional cosmologies in even-dimensional space-times (D=2n) containg perfect fluid and a multidimensional generalization of the Maxwell field, preserving its conformal invariance (the F field, an n-form). Among models…
This paper considers some physically interesting cosmological dynamical systems in the FRW-scalarfield category which are examined for integrability according to the criterion of Painlev\'e. In the literature these systems have been…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
We consider cosmological models with an arbitrary number of scalar fields nonminimally coupled to gravity and construct new integrable cosmological models. In the constructed models, the Ricci scalar is an integral of motion irrespectively…
The integrability of the\ $\Lambda-$Einstein-nonlinear $SU(2)$ $\sigma$-model with nonvanishing cosmological charge is studied. We apply the method of singularity analysis of differential equations and we show that the equations for the…
The singularity structure of cosmological models whose matter content consists of a scalar field with arbitrary non-negative potential is discussed. The special case of spatially flat FRW space-time is analysed in detail using a dynamical…
From higher dimensional theories, e.g. string theory, one expects the presence of non-minimally coupled scalar fields. We review the notion of conformal frames in cosmology and emphasize their physical equivalence, which holds at least at a…