Physics and cosmology in an inhomogeneous Universe

Abstract

Examples are presented of applications of the Lemaître -Tolman model to problems of astrophysics and gravitation theory. They are: 1. Inferring the spatial distribution of matter by interpretation of observations; 2. Interaction of inhomogeneities in matter distribution with the CMB radiation; 3. Evolution of voids; 4. Singularities; 5. Influence of electromagnetic field on gravitational collapse. This review is meant to demonstrate that the theory is already well-prepared to meet the challenges posed by an inhomogeneous Universe. Why consider inhomogeneous models?The more appropriate question here is: why not? We know that the FriedmannLemaître -Robertson -Walker (FLRW) models are a realistic first approximation to the geometry and physics of our Universe. We know (from many published examples, and see also below) that their generalizations are still reasonably simple. The urge to explore the unknown (once upon a time considered a necessary part of a scientist's personality) still lingers in the physics community. This should be a sufficient motivation for the beginning; more of it will appear along the way.In this article, only one class of models will be discussed, the Lemaître (1933) -Tolman (1934 (LT) models, and only a small selection of existing material will be presented. For a more complete treatment see the other review by this author (Krasiński 1997). The Lemaître -Tolman modelAssume that the Universe is isotropic around one observer, but not spatially homogeneous. (How to save the "cosmological principle" in such a model will be explained the end of this section.) Assume that the matter of the Universe is dust. In comoving coordinates, the metric form is then:The case R, r = 0 has to be considered separately and it leads to the solution found by Datt (1938, see also Krasiński 1997. It is an inhomogeneous generalization of the KantowskiSachs (1966) solution and has interesting geometrical properties, but has not been exploited 1

New non-separable diagonal cosmologies

“…With these explicit forms for the functions M and N, the partial differential equations (15) can be integrated to give Z 0 and therefore we can immediately calculate Z from its definition (14) and H from (11). The results are given by the following expressions (note that in the Solution I we have to distinguish between three subcases in order to perform explicitly the integral for H):…”

“…where the arbitrary constants b, c and H 0 come from the integration of the differential equations (14) and (11).…”

Relativistic Bessel cylinders

“…The 1917 solutions of Weyl and Levi-Civita are used for cylindrical vacuums [2][3][4], and there are a wide range of cylindrical matter solutions. Krasinski [5] has reviewed many of the cylindrical solutions with perfect and imperfect fluid sources. Other fluid descriptions include the 1937 van Stockum rotating dust solution [6], constant density string solutions [7,8], cylinders with a cosmological vacuum [9], and global solutions for static cylinders [10].…”

G1spacetimes with gravitational and scalar waves

“…These new sets of metrics will be generated starting from generalized vacuum Einstein-Rosen spacetimes, which admit an Abelian group of isometries G 2 acting transitively on spacelike surfaces. In the last decades there has been intensive study of G 2 vacuum and matter filled cosmological models and several major reviews on the subject have been written [9,10,8].…”