7. Z. Golda, A.Woszczyna
Dispersion of density waves in the early universe with positive cosmological constant
Class. Quantum Grav., vol. 20, p. 277 (2003).
[abstract] [preprint] [journal]

Abstract:
Density perturbations in the flat (K=0) Robertson-Walker universe with radiation ($p=\epsilon/3$) and positive cosmological constant ($\Lambda>0$) are investigated. The phenomenon of anomalous dispersion of acoustic waves on $\Lambda$ is discussed.

8. Zdzislaw A. Golda, Andrzej Woszczyna
A field theory approach to cosmological density perturbations
Phys. Lett. A , vol. 310, pp. 357-362 (2003).
[abstract] [preprint] [journal]

Abstract:
Adiabatic perturbations propagate in the expanding universe like scalar massless fields in some effective Robertson-Walker space-time.

9. Zdzislaw A. Golda, Andrzej Woszczyna
Acoustics of early universe. I. Flat versus open universe models
Class. Quant. Grav., vol. 18, pp. 543-554 (2001).
[abstract] [preprint] [journal]

Abstract:
A simple perturbation description unique for all signs of curvature, and based on the gauge-invariant formalisms is proposed to demonstrate that: (1) The density perturbations propagate in the flat radiation-dominated universe in exactly the same way as electromagnetic or gravitational waves propagate in the epoch of the matter domination. (2) In the open universe, sounds are dispersed by curvature. The space curvature defines the minimal frequency $\omega_{\rm c}$ below which the propagation of perturbations is forbidden. Gaussian acoustic fields are considered and the curvature imprint in the perturbations spectrum is discussed

10. Zdzislaw A. Golda, Andrzej Woszczyna
Acoustics of early universe. II. Lifshitz vs. gauge-invariant theories
J. Math. Phys., vol. 42, pp. 856-862 (2001).
[abstract] [preprint] [journal]

Abstract:
Appealing to classical methods of order reduction, we reduce the Lifshitz system to a second order differential equation. We demonstrate its equivalence to well known gauge-invariant results. For a radiation dominated universe we express the metric and density corrections in their exact forms and discuss their acoustic character.

11. 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.

12. 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.