13. Marco Litterio, Leszek M. Sokołowski, Zdzisław A. Golda, Luca Amendola, Andrzej Dyrek
Anisotropic inflation from extra dimensions
Phys. Lett., vol. B382, pp. 45-52 (1996).
[abstract] [preprint] [journal]

Abstract:
Vacuum multidimensional cosmological models with internal spaces being compact $n$-dimensional Lie group manifolds are considered. Products of 3-spheres and $SU(3)$ manifold (a novelty in cosmology) are studied. It turns out that the dynamical evolution of the internal space drives (power-law) inflation in the external world. This inflationary solution brings two extra bonuses: 1) it is an attractor in phase space (no fine-tuning required); 2) it is determined by the Lie group space solely and not by any arbitrary inflaton potentials. Only scalar fields representing the anisotropic scale factors of the internal space appears in the four dimensions. The size of the volume of the internal space at the end of inflation is compatible with observational constraints. This simple and natural model can be completed by some extended-inflation-like mechanism that ends the inflationary evolution.

14. Zdzisław A. Golda, Marco Litterio, Leszek M. Sokołowski, Luca Amendola, Andrzej Dyrek
Pure Geometrical Evolution of the Multidimensional Universe
Ann. Phys. , vol. 248, pp. 246-285 (1996).
[abstract] [journal]

Abstract:
An exhaustive qualitative analysis of cosmological evolution for some multidimensional universes is given. The internal space is taken to be a compact Lie group Riemannian manifold. The space is generically anisotropic; i.e., its cosmological evolution is described by its (time-dependent) volume, the dilaton, and by relative anisotropic deformation factors representing the shear of the internal dimensions during the evolution. Neither the internal space nor its subspaces need to be Einstein spaces. The total spacetime is empty, and the cosmic evolution of the external, four-dimensional world is driven by the geometric ``matter'' consisting of the dilaton and of the deformation factors. Since little is known about any form of matter in the extra dimensions, we do not introduce any {\it ad hoc\/} matter content of the Universe. We derive the four-dimensional Einstein field equations (with a cosmological term) for these geometric sources in full generality, i.e., for any compact Lie group. A detailed analysis is done for some specific internal geometries: products of 3-spheres, and $SU$(3) space. Asymptotic solutions exhibit power law inflation along with a process of full or partial isotropization. For the $SU$(3) space all the deformation factors tend to a common value, whereas in the case of $S^3$'s each sphere isotropizes separately.

15. Leszek M. Sokołowski, Zdzisław A. Golda, Marco Litterio, Luca Amendola
Classical instability of the Einstein-Gauss-Bonnet gravity theory with compactified higher dimensions
Int. J. Mod. Phys. , vol. A6, pp. 4517-4555 (1991).
[abstract] [journal]

Abstract:
The energy spectrum and stability of the effective theory resulting from the Einstein-Gauss-Bonnet gravity theory with compactified internal space are investigated. The internal space can evolve in its volume andór shape, giving rise to a system of scalar fields in the external space-time. The resulting scalar-tensor theory of gravity has physically unacceptable properties. First of all, the scalar fields’ energy is indefinite and unbounded from below, and thereby the gravitational and scalar fields form a self-exciting system. In contradistinction to the case of multidimensional Einstein gravity, this inherent instability of the effective theory cannot be removed by field redefinitions in the process of dimensional reduction (e.g. by a conformal rescaling of the metric in four dimensions, as is done in the former case). To get a viable effective gravity theory one should discard either the geometric scalar fields or the Gauss-Bonnet term from the Lagrangian of the multidimensional theory. It is argued that it is the Gauss-Bonnet term that should be discarded.

16. Marek Demiański, Zdzisław Golda, Waldemar Puszkarz
Dynamics of the D-dimensional FRW-cosmological Models within the Superstring-generated Gravity Model
Gen. Rel. Grav., vol. 23, pp. 917-939 (1991).
[abstract] [journal]

Abstract:
We study the dynamics of the generalized $D$-dimensional ($D = 1 + 3 + d$) Friedman-Robertson-Walker (FRW) cosmological models in the framework of an extended gravity theory obtained by adding the Gauss-Bonnet term to the standard Einstein-Hilbert action. In our discussion we extensively use methods of dynamical systems. We consider models filled in with a perfect fluid obeying the equation of state $p = (\gamma - 1)\rho$ and vacuum but non-flat models. We present a detailed analysis of the ten dimensional model and in particular we study the vacuum case. Several phase portraits show how the evolution of this model depends on the parameter $\gamma$.

17. M. Demianski, Z. A. Golda, M. Heller and M. Szydłowski
Kantowski-Sachs multidimensional cosmological models and dynamical dimensional reduction
Class. Quantum Grav., vol. 5, pp. 733-742 (1988).
[abstract] [journal]

Abstract:
Einstein's field equations are solved for a multidimensional spacetime $(KS)\times T^m$, where ($KS$) is a four-dimensional Kantowski-Sachs' spacetime (1966) and $T^m$ is an $m$-dimensional torus. Among all possible vacuum solutions there is a large class of spacetimes in which the macroscopic space expands and the microscopic space contracts to a finite volume. The authors also consider a non-vacuum case and they explicitly solve the field equations for the matter satisfying the Zel'dovich equations of state (1987). In non-vacuum models, with matter satisfying an equation of state $\rho = \gamma\rho$. $0\leq \gamma\leq 1$, at a sufficiently late stage of evolution the microspace always expands and the dynamical dimensional reduction does not occur. Models $(KS)\times B(IX)\times S^1\times S^1\times S^1\times S^1$ and $(KS)\times B(IX)\times B(IX)\times S^1$, where $B(IX)$ is the Bianchi type-$IX$ space, are also briefly discussed. It is shown that there is no chaotic behaviour in these cases. The same conclusion is also valid when one-loop high-temperature quantum corrections generated by a massless scalar field are taken into account.

18. Leszek M. Sokołowski, Zdzisław A. Golda
Instability of Kaluza-Klein cosmology
Phys. Lett., vol. B195, pp. 349-356 (1987).
[abstract] [journal]

Abstract:
We show that cosmological solutions in Kaluza-Klein theory in more than five dimensions are unstable. This is due to the fact that the extra cosmic scale factors appearing in the metric ansatz act as scalar matter fields in the physical four-dimensional spacetime. These fields have physically unacceptable features: their kinetic energy can be negative and the energy spectrum is unbounded from below. To remove the defects a reinterpretation of the cosmological metric ansatz is necessary.