Search

It has previously been shown heuristically that the topology of the Universe affects gravity, in the sense that a test particle near a massive object in a multiply connected universe is subject to a topologically induced acceleration that opposes the local attraction to the massive object. This effect distinguishes different comoving 3-manifolds, potentially providing a theoretical justification for the Poincar\'e dodecahedral space observational hypothesis and a dynamical test for cosmic topology. It is necessary to check if this effect occurs in a fully relativistic solution of the Einstein equations that has a multiply connected spatial section. A Schwarzschild-like exact solution that is multiply connected in one spatial direction is checked for analytical and numerical consistency with the heuristic result. The T$^1$ (slab space) heuristic result is found to be relativistically correct. For a fundamental domain size of $L$, a slow-moving, negligible-mass test particle lying at distance $x$ along the axis from the object of mass $M$ to its nearest multiple image, where $GM/c^2 \ll x \ll L/2$, has a residual acceleration away from the massive object of $4\zeta(3) G(M/L^3)\,x$, where $\zeta(3)$ is Ap\'ery's constant. For $M \sim 10^14 M_\odot$ and $L \sim 10$ to $20\hGpc$, this linear expression is accurate to $\pm10%$ over $3\hMpc \ltapprox x \ltapprox 2\hGpc$. Thus, at least in a simple example of a multiply connected universe, the topological acceleration effect is not an artefact of Newtonian-like reasoning, and its linear derivation is accurate over about three orders of magnitude in $x$., Comment: 12 pages, 2 figures, 1 table; v3: N-body simulation discussion removed, references added, minor errors corrected

We aim to improve the surface of last scattering (SLS) optimal cross-correlation method in order to refine estimates of the Poincar\'e dodecahedral space (PDS) cosmological parameters. We analytically derive the formulae required to exclude points on the sky that cannot be members of close SLS-SLS cross-pairs. These enable more efficient pair selection without sacrificing uniformity of the underlying selection process. In certain cases this decreases the calculation time and increases the number of pairs per separation bin. (i) We recalculate Monte Carlo Markov Chains (MCMC) on the five-year WMAP data; and (ii) we seek PDS solutions in a small number of Gaussian random fluctuation (GRF) simulations. For 5 < alpha/deg < 60, a calculation speed-up of 3-10 is obtained. (i) The best estimates of the PDS parameters for the five-year WMAP data are similar to those for the three-year data. (ii) Comparison of the optimal solutions found by the MCMC chains in the observational map to those found in the simulated maps yields a slightly stronger rejection of the simply connected model using $\alpha$ than using the twist angle $\phi$. The best estimate of $\alpha$ implies that_given a large scale auto-correlation as weak as that observed,_ the PDS-like cross-correlation signal in the WMAP data is expected with a probability of less than about 10%. The expected distribution of $\phi$ from the GRF simulations is approximately Gaussian around zero, it is not uniform on $[-\pi,\pi]$. We infer that for an infinite, flat, cosmic concordance model with Gaussian random fluctuations, the chance of finding_both_ (a) a large scale auto-correlation as weak as that observed,_and_ (b) a PDS-like signal similar to that observed is less than about 0.015% to 1.25%., Comment: 18 pages, 19 figures, accepted in Astronomy & Astrophysics, software available at http://cosmo.torun.pl/GPLdownload/dodec/ and MCMCs at http://cosmo.torun.pl/GPLdownload/MCMC/ ; v2: histograms added, several minor changes, matches accepted version

Several studies have proposed that the shape of the Universe may be a Poincare dodecahedral space (PDS) rather than an infinite, simply connected, flat space. Both models assume a close to flat FLRW metric of about 30% matter density. We study two predictions of the PDS model. (i) For the correct model, the spatial two-point cross-correlation function, $\ximc$, of temperature fluctuations in the covering space, where the two points in any pair are on different copies of the surface of last scattering (SLS), should be of a similar order of magnitude to the auto-correlation function, $\xisc$, on a single copy of the SLS. (ii) The optimal orientation and identified circle radius for a "generalised" PDS model of arbitrary twist $\phi$, found by maximising $\ximc$ relative to $\xisc$ in the WMAP maps, should yield $\phi \in \{\pm 36\deg\}$. We optimise the cross-correlation at scales < 4.0 h^-1 Gpc using a Markov chain Monte Carlo (MCMC) method over orientation, circle size and $\phi$. Both predictions were satisfied: (i) an optimal "generalised" PDS solution was found, with a strong cross-correlation between points which would be distant and only weakly correlated according to the simply connected hypothesis, for two different foreground-reduced versions of the WMAP 3-year all-sky map, both with and without the kp2 Galaxy mask: the face centres are $(l,b)_{i=1,6}\approx (184d, 62d), (305d, 44d), (46d, 49d), (117d, 20d), (176d, -4d), (240d, 13d) to within ~2d, and their antipodes; (ii) this solution has twist \phi= (+39 \pm 2.5)d, in agreement with the PDS model. The chance of this occurring in the simply connected model, assuming a uniform distribution $\phi \in [0,2\pi]$, is about 6-9%., Comment: 20 pages, 22 figures, accepted in Astronomy & Astrophysics, software available at http://adjani.astro.umk.pl/GPLdownload/dodec/ and MCMCs at http://adjani.astro.umk.pl/GPLdownload/MCMC