A residual acceleration effect due to an inhomogeneity

Abstract

The perturbed Friedmann-Lemaitre-Robertson-Walker models allow many different possibilities for the 3-manifold of the comoving spatial section of the Universe. It used to be thought that global properties of the spatial section, including the topology of the space, have no feedback effect on dynamics. However, an elementary, weak-limit calculation shows that in the presence of a density perturbation, a gravitational feedback effect that is algebraically similar to dark energy does exist. Moreover, the effect differs between different 3-spaces. Among the well-proportioned spaces, the effect disappears down to third order in several cases, and down to fifth order for the Poincare dodecahedral space S^3/I^*. The Poincare space, that which also is preferred in many observational analyses, is better-balanced than the other spaces.