103. 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.

104. 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

105. 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.

106. 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

107. Andrzej Woszczyna
Gauge invariant cosmic structures : A dynamic systems approach
Phys. Rev. D, vol. 45, pp. 1982-1988 (1992).
[abstract] [journal]

Abstract:
Gravitational instability is expressed in terms of the dynamic systems theory. The gauge-invariant Ellis-Bruni equation and Bardeen's equation are discussed in detail. It is shown that in an open universe filled with matter of constant sound velocity the Jeans criterion does not adequately define the length scale of the gravitational structure.

108. 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.