The use of world models with antipoles in deriving an upper bound for the cosmological dens1tv parameter
If our Universe can be adequately described by one of the isotropic zeropressure models arising from the field equations of general relativity (with the cosmological constant), then it corresponds to a point of a plane whose coordinates can be taken as the familiar acceleration and density parameters, q0 and a0. A large area corresponding to some of the singular `big-bang models can be ruled out by considering lower bounds for the age of the Universe, and most of the non-singular models are ruled out since observed redshifts are in excess of the theoretical maximum redshifts of these models. This still leaves an infinite area of the q , a0 diagram in which our Universe may lie, and an upper bound for the mean density of matter would reduce this to a finite region. However, the bounds obtained by most of the recent direct observational work are unsatisfactory, and this leaves an important gap in the available tests of cosmological models. The main conclusion of this paper is that the gap could be filled with the aid of a new test involving only those models with observable antipoles (models in which photons have had time to travel at least ` halfway round the Universe'). The proposed test is completely independent of density estimates.