18 research outputs found
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
A Counterexample to Claimed COBE Constraints on Compact Toroidal Universe Models
It has been suggested that if the Universe satisfies a flat, multiply
connected, perturbed Friedmann-Lema^itre model, then cosmic microwave
background data from the COBE satellite implies that the minimum size of the
injectivity diameter (shortest closed spatial geodesic) must be larger than
about two fifths of the horizon diameter. To show that this claim is
misleading, a simple universe model of injectivity diameter a
quarter of this size, i.e. a tenth of the horizon diameter, is shown to be
consistent with COBE four year observational maps of the cosmic microwave
background. This is done using the identified circles principle.Comment: 11 pages, 3 figures, accepted for Classical & Quantum Gravit
A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently
regained interest as a good fit to the observed cosmic microwave background
temperature fluctuations. However, it is generally thought that a globally,
exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a
probability space on the set F of compact, comoving, 3-spatial sections of FLRW
models, a physically motivated hypothesis is proposed, using the density
parameter Omega as a derived rather than fundamental parameter. We assume that
the processes that select the 3-manifold also select a global mass-energy and a
Hubble parameter. The inferred range in Omega consists of a single real value
for any 3-manifold. Thus, the obvious measure over F is the discrete measure.
Hence, if the global mass-energy and Hubble parameter are a function of
3-manifold choice among compact FLRW models, then probability spaces
parametrised by Omega do not, in general, give a zero probability of a flat
model. Alternatively, parametrisation by the injectivity radius r_inj ("size")
suggests the Lebesgue measure. In this case, the probability space over the
injectivity radius implies that flat models occur almost surely (a.s.), in the
sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3:
generalisation: m, H functions of
How well-proportioned are lens and prism spaces?
The CMB anisotropies in spherical 3-spaces with a non-trivial topology are
analysed with a focus on lens and prism shaped fundamental cells. The
conjecture is tested that well proportioned spaces lead to a suppression of
large-scale anisotropies according to the observed cosmic microwave background
(CMB). The focus is put on lens spaces L(p,q) which are supposed to be oddly
proportioned. However, there are inhomogeneous lens spaces whose shape of the
Voronoi domain depends on the position of the observer within the manifold.
Such manifolds possess no fixed measure of well-proportioned and allow a
predestined test of the well-proportioned conjecture. Topologies having the
same Voronoi domain are shown to possess distinct CMB statistics which thus
provide a counter-example to the well-proportioned conjecture. The CMB
properties are analysed in terms of cyclic subgroups Z_p, and new point of view
for the superior behaviour of the Poincar\'e dodecahedron is found
Cosmic Topology of Prism Double-Action Manifolds
The cosmic microwave background (CMB) anisotropies in spherical 3-spaces with
a non-trivial topology are studied. This paper discusses the special class of
the so-called double-action manifolds, which are for the first time analysed
with respect to their CMB anisotropies. The CMB anisotropies are computed for
all prism double-action manifolds generated by a binary dihedral and a cyclic
group with a group order of up to 180 leading to 33 different topologies.
Several spaces are found which show a suppression of the CMB anisotropies on
large angular distances as it is found on the real CMB sky. It turns out that
two of these spaces possess Dirichlet domains which are not very far from
highly symmetric polyhedra like Platonic or Archimedean ones
Hot pixel contamination in the CMB correlation function?
Recently, it was suggested that the map-making procedure, which is applied to
the time-ordered CMB data by the WMAP team, might be flawed by hot pixels. This
could lead to a bias in the pixels having an angular distance of about 141
degrees from hot pixels due to the differential measuring process of the
satellite WMAP. Here, the bias is confirmed, and the temperature two-point
correlation function C(theta) is reevaluated by excluding the affected pixels.
It is shown that the most significant effect occurs in C(theta) at the largest
angles near theta = 180 degrees. Furthermore, the corrected correlation
function C(theta) is applied to the cubic topology of the Universe, and it is
found that such a multi-connected universe matches the temperature correlation
better than the LCDM concordance model, provided the cubic length scale is
close to L=4 measured in units of the Hubble length
Cosmic Topology of Polyhedral Double-Action Manifolds
A special class of non-trivial topologies of the spherical space S^3 is
investigated with respect to their cosmic microwave background (CMB)
anisotropies. The observed correlations of the anisotropies on the CMB sky
possess on large separation angles surprising low amplitudes which might be
naturally be explained by models of the Universe having a multiconnected
spatial space. We analysed in CQG 29(2012)215005 the CMB properties of prism
double-action manifolds that are generated by a binary dihedral group D^*_p and
a cyclic group Z_n up to a group order of 180. Here we extend the CMB analysis
to polyhedral double-action manifolds which are generated by the three binary
polyhedral groups (T^*, O^*, I^*) and a cyclic group Z_n up to a group order of
1000. There are 20 such polyhedral double-action manifolds. Some of them turn
out to have even lower CMB correlations on large angles than the Poincare
dodecahedron
Three-dimensional Topology-Independent Methods to Look for Global Topology
The space-like hypersurface of the Universe at the present cosmological time
is a three-dimensional manifold. A non-trivial global topology of this
space-like hypersurface would imply that the apparently observable universe
(the sphere of particle horizon radius) could contain several images of the
single, physical Universe. Recent three-dimensional techniques for constraining
and/or detecting this topology are reviewed. Initial applications of these
techniques using X-ray bright clusters of galaxies and quasars imply (weak)
candidates for a non-trivial topology.Comment: minor revision; 7 pages, 1 figure, accepted by Classical and Quantum
Gravit
Topological Lensing in Spherical Spaces
This article gives the construction and complete classification of all
three-dimensional spherical manifolds, and orders them by decreasing volume, in
the context of multiconnected universe models with positive spatial curvature.
It discusses which spherical topologies are likely to be detectable by
crystallographic methods using three-dimensional catalogs of cosmic objects.
The expected form of the pair separation histogram is predicted (including the
location and height of the spikes) and is compared to computer simulations,
showing that this method is stable with respect to observational uncertainties
and is well suited for detecting spherical topologies.Comment: 32 pages, 26 figure
Constraints on the Detectability of Cosmic Topology from Observational Uncertainties
Recent observational results suggest that our universe is nearly flat and
well modelled within a CDM framework. The observed values of
and inevitably involve uncertainties. Motivated
by this, we make a systematic study of the necessary and sufficient conditions
for undetectability as well as detectability (in principle) of cosmic topology
(using pattern repetition) in presence of such uncertainties. We do this by
developing two complementary methods to determine detectability for nearly flat
universes. Using the first method we derive analytical conditions for
undetectability for infinite redshift, the accuracy of which is then confirmed
by the second method. Estimates based on WMAP data together with other
measurements of the density parameters are used to illustrate both methods,
which are shown to provide very similar results for high redshifts.Comment: 16 pages, 1 figure, LaTeX2