168 research outputs found
Topology of the Universe: background and recent observational approaches
Is the Universe (a spatial section thereof) finite or infinite? Knowing the
global geometry of a Friedmann-Lema\^{\i}tre (FL) universe requires knowing
both its curvature and its topology. A flat or hyperbolic (``open'') FL
universe is {\em not} necessarily infinite in volume.
Multiply connected flat and hyperbolic models are, in general, as consistent
with present observations on scales of 1-20{\hGpc} as are the corresponding
simply connected flat and hyperbolic models. The methods of detecting multiply
connected models (MCM's) are presently in their pioneering phase of development
and the optimal observationally realistic strategy is probably yet to be
calculated. Constraints against MCM's on ~1-4 h^{-1} Gpc scales have been
claimed, but relate more to inconsistent assumptions on perturbation statistics
rather than just to topology. Candidate 3-manifolds based on hypothesised
multiply imaged objects are being offered for observational refutation.
The theoretical and observational sides of this rapidly developing subject
have yet to make any serious contact, but the prospects of a significant
detection in the coming decade may well propel the two together.Comment: 5 pages, proceedings of the Workshop ``Cosmology: Observations
Confront Theories,'' 11-17 Jan 1999, IIT Kharagpur, West Bengal, to appear in
Pramana - Journal of Physic
Transverse Galaxy Velocities from Multiple Topological Images
The study of the kinematics of galaxies within clusters or groups has the
limitation that only one of the three velocity components and only two of the
three spatial components of a galaxy position in six-dimensional phase space
can normally be measured. However, if multiple topological images of a cluster
exist, then the radial positions and sky plane mean velocities of galaxies in
the cluster may also be measurable from photometry of the two cluster images.
The vector arithmetic and principles of the analysis are presented. These are
demonstrated by assuming the suggested topological identification of the
clusters RX J1347.5-1145 and CL 09104+4109 to be correct and deducing the
sky-plane relative velocity component along the axis common to both images of
this would-be single cluster.
Three out of four of the inferred transverse velocities are consistent with
those expected in a rich cluster. A control sample of random `common' sky-plane
axes, independent of the topological hypothesis, implies that this is not
surprising. This shows that while galaxy kinematics are deducible from
knowledge of cosmological topology, it is not easy to use them to refute a
specific candidate manifold.Comment: 13 pages, 7 figures, accepted for MNRA
Does gravity prefer the Poincare dodecahedral space?
The missing fluctuations problem in cosmic microwave background observations
is naturally explained by well-proportioned small universe models. Among the
well-proportioned models, the Poincare dodecahedral space is empirically
favoured. Does gravity favour this space? The residual gravity effect is the
residual acceleration induced by weak limit gravity from multiple topological
images of a massive object on a nearby negligible mass test object. At the
present epoch, the residual gravity effect is about a million times weaker in
three of the well-proportioned spaces than in ill-proportioned spaces. However,
in the Poincare space, the effect is 10,000 times weaker still, i.e. the
Poincare space is about 10^{10} times "better balanced" than ill-proportioned
spaces. Both observations and weak limit dynamics select the Poincare space to
be special.Comment: 6 pages, Honorable Mention in 2009 Gravity Research Foundation essay
competitio
The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
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 , found by
maximising \ximc relative to \xisc in the WMAP maps, should yield . 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 . 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
\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/MCM
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