Energy of Einstein's static universe and its implications for the ΛCDM cosmology

Abstract

The total Einstein energy (P0) of a homogeneous and isotropic universe can be computed by using an appropriate superpotential (Rosen 1994) and also by a direct method (Mitra 2010). Irrespective of the physical significance of P0, its eventual numerical value must be same in both the cases because both are derived from the same Einstein pseudo tensor and by employing the same coordinates. It follows then that the static isotropic and homogeneous universe, i.e., Einstein's static universe (ESU), must have an infinite radius and which tantamounts to a spatially flat case. The physical significance of this result is that the cosmological constant, Λ, is actually zero and ESU is the vacuous Minkowski spacetime. It is the same result which has recently been obtained in a completely independent manner (Mitra, Bhattacharyya & Bhatt 2013). Thus even though, mathematically, one can conceive of a static 3-sphere for the foundation of relativistic cosmology, physically, no such 3-sphere exists. On the other hand, the spatial section of the universe could essentially be an Euclidean space with local curvature spikes due to presence of lumpy matter. Since the ``Dark Energy'' is associated with Λ in the ΛCDM model, the result obtained here suggests that it is an artifact of departure of the lumpy and fractal universe from the ideal Friedmann Robertson Walker model (Jackson et al. 2012, Cowley et al. 2013).