A New Type of Exact Arbitrarily Inhomogeneous Cosmology: Evolution of Deceleration in the Flat Homogeneous-On-Average Case

A new method for constructing exact inhomogeneous universes is presented, that allows variation in 3 dimensions. The resulting spacetime may be statistically uniform on average, or have random, non-repeating variation. The construction utilises the Darmois junction conditions to join many different component spacetime regions. In the initial simple example given, the component parts are spatially flat and uniform, but much more general combinations should be possible. Further inhomogeneity may be added via swiss cheese vacuoles and inhomogeneous metrics. This model is used to explore the proposal, that observers are located in bound, non-expanding regions, while the universe is actually in the process of becoming void dominated, and thus its average expansion rate is increasing. The model confirms qualitatively that the faster expanding components come to dominate the average, and that inhomogeneity results in average parameters which evolve differently from those of any one component, but more realistic modelling of the effect will need this construction to be generalised.Comment: JCAP Latex, 14pp, 2 figures(2nd with 5 plots), 4 table

Comment on `Smooth and Discontinuous Signature Type Change in General Relativity'

Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slightly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is possible to have a bounded energy-momentum tensor at a change of signature without satisfying their condition that the extrinsic curvature vanish.Comment: Plain TeX, 6 pages; Comment on Kossowski and Kriele: Class. Quantum Grav. 10, 2363 (1993); Reply by Kriele: Gen. Rel. Grav. 28, 1409-1413 (1996

More examples of structure formation in the Lemaitre-Tolman model

In continuing our earlier research, we find the formulae needed to determine the arbitrary functions in the Lemaitre-Tolman model when the evolution proceeds from a given initial velocity distribution to a final state that is determined either by a density distribution or by a velocity distribution. In each case the initial and final distributions uniquely determine the L-T model that evolves between them, and the sign of the energy-function is determined by a simple inequality. We also show how the final density profile can be more accurately fitted to observational data than was done in our previous paper. We work out new numerical examples of the evolution: the creation of a galaxy cluster out of different velocity distributions, reflecting the current data on temperature anisotropies of CMB, the creation of the same out of different density distributions, and the creation of a void. The void in its present state is surrounded by a nonsingular wall of high density.Comment: LaTeX 2e with eps figures. 30 pages, 11 figures, 30 figure files. Revision matches published versio