Related papers: Integrability and explicit solutions in some Bianc…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
A spatially homogeneous and locally rotationally symmetric Bianchi type-II cosmological model under the influence of both shear and bulk viscosity has been studied. Exact solutions are obtained with a barotropic equation of state between…
Using the methods developed for different Bianchi class A cosmological models we treat the simplest Bianchi class B model, namely Bianchi type V. The future non-linear stability for solutions of the Einstein-Vlasov system is demonstrated…
In a recent paper arXiv:1208.4231 we have treated the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. We have been able now to remove the reflection symmetry…
We describe a class of integrable models of 1+1 and 1-dimensional dilaton gravity coupled to scalar fields. The models can be derived from high dimensional supergravity theories by dimensional reductions. The equations of motion of these…
Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This…
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 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 present an approach to higher dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators. Specifically, working with the…
The application of the Darboux Transformation method to the integrable model of Cylindrically Symmetrical Chiral field has been considered. The associated linear system of matrix equations has been proposed and the properties of symmetrie…
We investigate the isometrically embedded Bianchi type-V cosmology braneworld model in a $D$-dimensional bulk space. The model provides a fluid of geometric dark energy (GDE) and unification of fundamental forces similar to the…
We consider $G_2$-structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi…
In this paper we analyze the tangential symmetries of Darboux integrable decomposable exterior differential systems. The decomposable systems generalize the notion of a hyperbolic exterior differential system and include the classic notion…
In this paper the dynamics of free gauge fields in Bianchi type I-VII$_{h}$ space-times is investigated. The general equations for a matter sector consisting of a $p$-form field strength ($p\,\in\,\{1,3\}$), a cosmological constant…
Multidimensional cosmological models with $n (n > 1)$ spaces of constant curvature are discussed classically and with respect to canonical quantization. These models are integrable in the case of Ricci flat internal spaces. For positive…
Einstein equations for several matter sources in homogeneous, isotropic metric are shown to reduce to a second order nonlinear ordinary differential equation. An analysis of its solutions is made in an important case.
The solvable Bianchi I-VII groups which arise as homogeneity groups in cosmological models are analyzed in a uniform manner. The dual spaces (the equivalence classes of unitary irreducible representations) of these groups are computed…
We investigate the three types of class B Bianchi cosmologies filled with a tilted perfect fluid undergoing velocity diffusion in a scalar field background. We consider the two most importantcases: dust and radiation. A complete numerical…
For the quadratic Poincar\'e gauge theory of gravity (PG) we consider the FLRW cosmologies using an isotropic Bianchi representation. Here the considered cosmologies are for the general case: all the even and odd parity terms of the…
Within the scope of Bianchi type VI (BVI) model the self-consistent system of nonlinear spinor and gravitational fields is considered. Exact self-consistent solutions to the spinor and gravitational field equations are obtained for some…