Conformally Friedmann-Lemaitre-Robertson-Walker cosmologies

Abstract: In a universe where, according to the standard cosmological models, some 97% of the total mass-energy is still "missing in action" it behooves us to spend at least a little effort critically assessing and exploring radical alternatives. Among possible, (dare we say plausible), nonstandard but superficially viable models, those spacetimes conformal to the standard Friedmann-Lemaitre-Robertson-Walker class of cosmological models play a very special role --- these models have the unique and important property of permitting large non-perturbative geometric deviations from Friedmann-Lemaitre-Robertson-Walker cosmology without unacceptably distorting the cosmic microwave background. Performing a "cosmographic" analysis, (that is, temporarily setting aside the Einstein equations, since the question of whether or not the Einstein equations are valid on galactic and cosmological scales is essentially the same question as whether or not dark matter/dark energy actually exist), and using both supernova data and information about galactic structure, one can nevertheless place some quite significant observational constraints on any possible conformal mode --- however there is still an extremely rich range of phenomenological possibilities for both cosmologists and astrophysicists to explore.