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103. David H Lyth, Andrzej Woszczyna Large scale perturbations in the open universe Phys. Rev. D, vol. 52, pp. 33383357 (1995). [abstract] [preprint] [journal]  Abstract: When considering perturbations in an open (Omega<1) universe, cosmologists retain only subcurvature modes (defined as eigenfunctions of the Laplacian whose eigenvalue is less than 1 in units of the curvature scale, in contrast with the supercurvature 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 subcurvature 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 supercurvature modes in nature. Finally the effect on the cmb of any supercurvature 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 scalartensor 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 selfinteracting scalar field. Physically they describe a massless spin2 field (graviton) and a spin0 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. 50395059 (1994). [abstract] [preprint] [journal]  Abstract: We argue that in a nonlinear gravity theory, which according to wellknown results is dynamically equivalent to a selfgravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent generalrelativistic 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 secondorder 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. 19821988 (1992). [abstract] [journal]  Abstract: Gravitational instability is expressed in terms of the dynamic systems theory. The gaugeinvariant EllisBruni 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 EinsteinGaussBonnet gravity theory with compactified higher dimensions Int. J. Mod. Phys. , vol. A6, pp. 45174555 (1991). [abstract] [journal]  Abstract: The energy spectrum and stability of the effective theory resulting from the EinsteinGaussBonnet 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 spacetime. The resulting scalartensor 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 selfexciting 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 GaussBonnet term from the Lagrangian of the multidimensional theory. It is argued that it is the GaussBonnet term that should be discarded.  
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