English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In a flat space, the global topology of comoving space can induce a weakacceleration effect similar to dark energy. Does a similar effect occur in thecase of the Poincare dodecahedral space S^3/I^*? Does the effect distinguishthe Poincare space from other well-proportioned spaces? The residualacceleration effect in the Poincare space is studied here using a massiveparticle and a nearby test particle of negligible mass, in S^3 embedded in R^4.The weak limit gravitational attraction on a test particle at distance r is set\propto [r_C \sin(r/r_C)]^{-2}, where r_C = curvature radius, in order tosatisfy Stokes' theorem. A finite particle horizon large enough to include theadjacent topological images of the massive particle is assumed. The regular,flat, 3-torus T^3 is re-examined, and two other well-proportioned spaces,S^3/T^* and S^3/O^*, are also studied. The residual gravity effect occurs inall four cases. In a perfectly regular 3-torus of side length L_a, and inS^3/T^* and S^3/O^*, the highest order term in the residual acceleration is thethird order term in the Taylor expansion of r/L_a (3-torus), or r/r_C,respectively. However, the Poincare dodecahedral space is unique among the fourspaces. The third order cancels, leaving the fifth order term \sim \pm 300(r/r_C)^5 as the most significant. Not only are three of the four perfectlyregular well-proportioned spaces better balanced than most other multiplyconnected spaces in terms of the residual acceleration effect by a factor ofabout a million (setting r/L_a = r/r_C \sim 10^{-3}), but the fourth of thesespaces is about 10^4 times better balanced than the other three. This is thePoincare dodecahedral space. Is this unique dynamical property of the Poincarespace a clue towards a theory of cosmic topology?

The residual gravity acceleration effect in the Poincare dodecahedral space