85. 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.

86. 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.

87. David H Lyth, Andrzej Woszczyna
Large scale perturbations in the open universe
Phys. Rev. D, vol. 52, pp. 3338-3357 (1995).
[abstract] [preprint] [journal]

Abstract:
When considering perturbations in an open (Omega<1) universe, cosmologists retain only sub-curvature modes (defined as eigenfunctions of the Laplacian whose eigenvalue is less than -1 in units of the curvature scale, in contrast with the super-curvature modes whose eigenvalue is between -1 and 0). Mathematicians have known for almost half a century that all modes must be included to generate the most general HOMOGENEOUS GAUSSIAN RANDOM FIELD, despite the fact that any square integrable FUNCTION can be generated using only the sub-curvature modes. The former mathematical object, not the latter, is the relevant one for physical applications. The mathematics is here explained in a language accessible to physicists. Then it is pointed out that if the perturbations originate as a vacuum fluctuation of a scalar field there will be no super-curvature modes in nature. Finally the effect on the cmb of any super-curvature contribution is considered, which generalizes to Omega<1 the analysis given by Grishchuk and Zeldovich in 1978. A formula is given, which is used to estimate the effect. In contrast with the case Omega=1, the effect contributes to all multipoles, not just to the quadrupole. It is important to find out whether it has the same l dependence as the data, by evaluating the formula numerically.

88. Leszek M. Sokołowski
Universality of Einstein's General Relativity
GR14 Conference (Florence, Italy, Aug 1995) (1995).
[abstract] [preprint] [journal]

Abstract:
Among relativistic theories of gravitation the closest ones to general relativity are the scalar-tensor ones and these with Lagrangians being any function f(R) of the curvature scalar. A complete chart of relationships between these theories and general relativity can be delineated. These theories are mathematically (locally) equivalent to general relativity plus a minimally coupled self-interacting scalar field. Physically they describe a massless spin-2 field (graviton) and a spin-0 component of gravity. It is shown that these theories are either physically equivalent to general relativity plus the scalar or flat space is classically unstable (or at least suspected of being unstable). In this sense general relativity is universal: it is an isolated point in the space of gravity theories since small deviations from it either carry the same physical content as it or give rise to physically untenable theories

89. Guido Magnano, Leszek M. Sokołowski
On Physical Equivalence between Nonlinear Gravity Theories
Phys. Rev. D, vol. 50, pp. 5039-5059 (1994).
[abstract] [preprint] [journal]

Abstract:
We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical. We explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system.

90. Andrzej Woszczyna
A dynamical systems approach to the cosmological structure formation - Newtonian universe
Mon. Not. R.A.S., vol. 225, p. 701 (1992).
[journal]

Abstract:
Abstract