Some more methods and exact solutions to solve Kaluza-Klein cosmologies

Abstract

The authors consider general methods to solve the equations for Kaluza-Klein cosmological models by using the formal identity of these equations with those of a relativistic point particle in a scalar field. The formal scalar field is given by the phenomenological matter content of the cosmological model in dependence of the difference expansion factors. They find general solutions for one- and two-component matter and general properties of such models.

On the Adiabatic Expansion of the Visible Space in a Higher-Dimensional Cosmology

“…Hence, there exist two equations of state in the form p d = p d (ρ), one for each subspace of dimensions d [23]. Once the overall matter-energy density ρ is properly defined, the form of the associated pressures, p ext and p int , may be directly obtained in terms of those equations [10]. In four dimensions the general linear equation of state…”

Kasner‐like, inflationary and steady‐state solutions in multi‐dimensional cosmology

“…massive monopoles, strings and so on, from the excitations in the internal spaces which occur in the external space as massive particles (pyrgons - Slansky 1984, Bleyer andZhuk 1995), or from the amplification of perturbation modes during the contraction of internal spaces Liebscher 1985, Bleyer et al 1991).…”

“…Due to this property we can call this model a steady-state model (Bondi and Gold 1948 (Ivashchuk et al 1989). A generalization to the case of coupling with quantum matter was given in Bleyer et al (1990). These are integrable models in the case the classical models are integrable.…”

Integration ofD-dimensional cosmological models with two factor spaces by reduction to the generalized Emden-Fowler equation

“…It should be mentioned that using of a basis in the form (3.1) provides the factorization of the potential (3.11) with respect to the coordinates of the vector x(t) (the additional linear transformation (3.7),(3.8) does not matter in this situation). Such factorization of the potential is essential under the developing of the following procedure proposed in [1]. Using the equation of motion following from the Lagrangian (3.9) we obtain the following second-order ordinary differential equation…”