Undermining the cosmological principle: almost isotropic observations in inhomogeneous cosmologies

We challenge the widely held belief that the cosmological principle is an o bvious consequence of the observed isotropy of the cosmic microwave backgro und radiation (CMB), combined with the Copernican principle. We perform a d etailed analysis of a class of inhomogeneous perfect fluid cosmologies admi tting an isotropic radiation field, with a view to assessing their viabilit y as models of the real universe. These spacetimes are distinguished from F LRW universes by the presence of inhomogeneous pressure, which results in a n acceleration of the fluid (fundamental observers). We examine their physi cal, geometrical and observational characteristics for all observer positio ns in the spacetimes. To this end, we derive exact, analytic expressions fo r the distance-redshift relations and anisotropies for any observer, and co mpare their predictions with available observational constraints. As far as the authors are aware, this work represents the first exact analysis of th e observational properties of an inhomogeneous cosmological model for all o bserver positions. Considerable attention is devoted to the anisotropy in t he CMB. The difficulty of defining the surface of last scattering in exact, inhomogenous cosmological models is discussed; several alternative practic al definitions are presented, and one of these is used to estimate the CMB anisotropy for any model. The isotropy constraints derived from 'local' obs ervations (redshift less than or similar to 1) are also considered, qualita tively. A crucial aspect of this work is the application of the Copernican principle: for a specific model to be acceptable we demand that it must be consistent with current observational constraints (especially anisotropy co nstraints) for all observer locations. The most important results of the pa per are presented as exclusion plots in the two-dimensional parameter space of the models. We show that there is a region of parameter space not ruled out by the constraints we consider and containing models that are signific antly inhomogeneous. It follows immediately from this that the cosmological principle cannot be assumed to hold on the basis of present observational constraints.