Dispersive Friedmann universes and synchronization

Abstract

We introduce consideration of dispersive aspects of standard perfect fluid Friedmann cosmology and study the new qualitative behaviours of cosmological solutions that emerge as the fluid parameter changes and zero eigenvalues appear in the linear part of the Friedmann equations. We find that due to their insufficient degeneracy, the Milne, flat, Einstein-static, and de Sitter solutions cannot properly bifurcate. However, the dispersive versions of Milne and flat universes contained in the versal unfolding of the standard Friedmann equations possess novel long-term properties not met in their standard counterparts. We apply these results to the horizon problem and show that unlike their hyperbolic versions, the dispersive Milne and flat solutions completely synchronize in the future, hence offering a solution to the homogeneity, isotropy, and causal connectedness puzzles.