Related papers: Multidimensional Integrable Cosmological Models wi…

For three dimensional complete, non-compact Riemannian manifolds with non-negative Ricci curvature and uniformly positive scalar curvature, we obtain the sharp linear volume growth ratio and the corresponding rigidity.

A class of cosmological solutions of higher dimensional Einstein field equations with the energy-momentum tensor of a homogeneous, isotropic fluid as the source are considered with an anisotropic metric that includes the direct sum of a…

A cosmological model based on Kaluza-Klein theory is studied. A metric, in which the scale factor of the compact space evolves as an inverse power of the radius of the observable universe, is constructed. The Freedmann-Robertson-Walker…

We consider general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature. We investigate the far future evolution of the universe in such models,…

A multidimensional cosmological model describing the dynamics of n+1 Ricci-flat factor-spaces M_i in the presence of a one-component anisotropic fluid is considered. The pressures in all spaces are proportional to the density: p_i = w_i…

Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To…

We consider a multidimensional cosmological model with nonlinear quadratic $R^2$ and quartic $R^4$ actions. As a matter source, we include a monopole form field, D-dimensional bare cosmological constant and tensions of branes located in…

Consider multidim. universes M= R x M_1 x ... x M_n with D = 1+ d_1 .. + d_n, where M_i of dimension d_i are of have constant curvature and compact for i>1. For Lagrangian models L(R,phi) on M which depend only on Ricci curvature R and a…

Let $M$ be a topological spherical space form, i.e. a smooth manifold whose universal cover is a homotopy sphere. We determine the number of path components of the space and moduli space of Riemannian metrics with positive scalar curvature…

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…

Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…

A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…

In this paper we first derive solutions which can be interpreted as branes wrapping nontrivial curved manifolds, and then study their cosmological implications. We find that at early times the branes tend to shrink the internal manifold,…

We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…

Various physical properties of cosmological models in (1+1) dimensions are investigated. We demonstrate how a hot big bang and a hot big crunch can arise in some models. In particular, we examine why particle horizons do not occur in matter…

We study some aspects of dynamical compactification scenario where stabilisation of extra dimensions occurs due to presence the Gauss-Bonnet term and non-zero spatial curvature. In the framework of the model under consideration there exists…

Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…

A multidimensional cosmology with FRW type metric having 4-dimensional space-time and $d$-dimensional Ricci-flat internal space is considered with a higher dimensional cosmological constant. The classical cosmology in commutative and…

The continuous 1D defects of an isotropic homogeneous material in a flat 3D space are classified by the Volterra process construction method. We employ the same method to classify the continuous 2D defects of a vacuum in a 4D maximally…

The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states…