Topological acceleration in relativistic cosmology

Abstract

Heuristic approaches in cosmology bypass more difficult calculations that would more strictly agree with the standard Einstein equation. These give us the well-known Friedmann-Lemaitre-Robertson-Walker (FLRW) models, and, more recently, the feedback effect of the global topology of spatial sections on the acceleration of test particles. Forcing the FLRW heuristic model on observations leads to dark energy, which, pending fully relativistic calculations, is best interpreted as an artefact. Could topological acceleration also be an artefact of using a heuristic approach? A multiply connected exact solution of the Einstein equation shows that topological acceleration is present in at least one fully relativistic case---it is not an artefact of Newtonian-like thinking.