A weak acceleration effect due to residual gravity in a multiply connected universe

Abstract

Could cosmic topology imply dark energy? We use a weak field (Newtonian) approximation of gravity and consider the gravitational effect from distant, multiple copies of a large, collapsed (virialised) object today (i.e. a massive galaxy cluster), taking into account the finite propagation speed of gravity, in a flat, multiply connected universe, and assume that due to a prior epoch of fast expansion (e.g. inflation), the gravitational effect of the distant copies is felt locally, from beyond the naively calculated horizon. We find that for a universe with a $T^{1}x{R}^2$ spatial section, the residual Newtonian gravitational force (to first order) provides an anisotropic effect that repels test particles from the cluster in the compact direction, in a way algebraically similar to that of dark energy. For a typical test object at comoving distance $\chi$ from the nearest dense nodes of the cosmic web of density perturbations, the pressure-to-density ratio $w$ of the equation of state in an FLRW universe, is w \sim - (χ/L)^3, where $L$ is the size of the fundamental domain, i.e. of the universe. Clearly, |w|<<1. For a T^3 spatial section of exactly equal fundamental lengths, the effect cancels to zero. For a T^3 spatial section of unequal fundamental lengths, the acceleration effect is anisotropic in the sense that it will *tend to equalise the three fundamental lengths*. Provided that at least a modest amount of inflation occurred in the early Universe, and given some other conditions, multiple connectedness does generate an effect similar to that of dark energy, but the amplitude of the effect at the present epoch is too small to explain the observed dark energy density and its anisotropy makes it an unrealistic candidate for the observed dark energy.

12 pages, 8 figures, accepted by Astronomy & Astrophysics; v2 includes 3D calculation and result; v3 includes analysis of numerical simulation, matches accepted version

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Cited by in corpus (19)

• The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
• Virialisation-induced curvature as a physical explanation for dark energy
• Solving the Einstein constraints in periodic spaces with a multigrid approach
• Promise of Future Searches for Cosmic Topology
• The study of topology of the universe using multipole vectors
• The residual gravity acceleration effect in the Poincare dodecahedral space
• Gauss-Bonnet-Chern approach to the averaged Universe
• The size of the Universe according to the Poincare dodecahedral space hypothesis
• On non-Euclidean Newtonian theories and their cosmological backreaction
• A relativistic model of the topological acceleration effect
• Gravitational potential in spherical topologies
• A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
• Homotopy symmetry in the multiply connected twin paradox of special relativity
• Topological implications of inhomogeneity
• Which FLRW comoving 3-manifold is preferred observationally and theoretically?
• There was movement that was stationary, for the four-velocity had passed around
• Dark energy as a spatial continuity condition
• Does gravity prefer the Poincare dodecahedral space?
• Some spaces are more equal than others