48 research outputs found
Topological signatures in CMB temperature anisotropy maps
We propose an alternative formalism to simulate CMB temperature maps in
CDM universes with nontrivial spatial topologies. This formalism
avoids the need to explicitly compute the eigenmodes of the Laplacian operator
in the spatial sections. Instead, the covariance matrix of the coefficients of
the spherical harmonic decomposition of the temperature anisotropies is
expressed in terms of the elements of the covering group of the space. We
obtain a decomposition of the correlation matrix that isolates the topological
contribution to the CMB temperature anisotropies out of the simply connected
contribution. A further decomposition of the topological signature of the
correlation matrix for an arbitrary topology allows us to compute it in terms
of correlation matrices corresponding to simpler topologies, for which closed
quadrature formulae might be derived. We also use this decomposition to show
that CMB temperature maps of (not too large) multiply connected universes must
show ``patterns of alignment'', and propose a method to look for these
patterns, thus opening the door to the development of new methods for detecting
the topology of our Universe even when the injectivity radius of space is
slightly larger than the radius of the last scattering surface. We illustrate
all these features with the simplest examples, those of flat homogeneous
manifolds, i.e., tori, with special attention given to the cylinder, i.e.,
topology.Comment: 25 pages, 7 eps figures, revtex4, submitted to PR
Can We See the Shape of the Universe?
This is a written version of a talk given at the Fifth Friedmann Seminar on
recent work in Observational Cosmic Topology done in partial collaboration with
Armando Bernui. We address three relevant questions related to the search for
the size and shape of our Universe: (i) How do the actual observation of
multiple images of certain cosmic objects, e.g. galaxy clusters, constrain the
possible models for the shape of our Universe?, (ii) What kind of predictions
can be done once a pair of cosmic objects have been identified to be
topological images related by a translation?, and (iii) Is it possible to
determine if two regions of space are topologically identified, even when
distortions on the distributions of cosmic sources due to observational
limitations are not negligible? We give examples answering the first two
questions using the suggestion of Roukema and Edge that the clusters RXJ
1347.5-1145 and CL 09104+4109 might be topological images of the Coma cluster.
For the third question, we suggest a method based on the analysis of PSH's
noise correlations which seems to give a positive answer.Comment: 6 pages, latex2e, contribution to the 5th Alexander Friedmann Seminar
on Gravitation and Cosmology, to appear in Int. J. Mod. Phys. A (2002).
Macros: ws-ijmpa.cl
Spikes in Cosmic Crystallography
If the universe is multiply connected and small the sky shows multiple images
of cosmic objects, correlated by the covering group of the 3-manifold used to
model it. These correlations were originally thought to manifest as spikes in
pair separation histograms (PSH) built from suitable catalogues. Using
probability theory we derive an expression for the expected pair separation
histogram (EPSH) in a rather general topological-geometrical-observational
setting. As a major consequence we show that the spikes of topological origin
in PSH's are due to translations, whereas other isometries manifest as tiny
deformations of the PSH corresponding to the simply connected case. This result
holds for all Robertson-Walker spacetimes and gives rise to two basic
corollaries: (i) that PSH's of Euclidean manifolds that have the same
translations in their covering groups exhibit identical spike spectra of
topological origin, making clear that even if the universe is flat the
topological spikes alone are not sufficient for determining its topology; and
(ii) that PSH's of hyperbolic 3-manifolds exhibit no spikes of topological
origin. These corollaries ensure that cosmic crystallography, as originally
formulated, is not a conclusive method for unveiling the shape of the universe.
We also present a method that reduces the statistical fluctuations in PSH's
built from simulated catalogues.Comment: 25 pages, LaTeX2e. References updated. To appear in Int. J. Mod.
Phys. D (2002) in the present for
A Note on the Robustness of Pair Separations Methods in Cosmic Topology
The pair separations statistical methods devised to detect the topology of
the universe rely on the accurate knowledge of the three-dimensional positions
of the cosmic sources. The determination of these positions, however, involves
inevitable observational uncertainties. The only significant (measurable) sign
of a nontrivial topology in PSH's was shown to be spikes. We briefly report our
results concerning the sensitivity of the topological spikes in the presence of
the uncertainties in the positions of the cosmic sources, which arise from
uncertainties in the values of the density parameters.Comment: To appear in the Proc. of 10th Marcel Grossmann Meeting on General
Relativity. Latex2e, World Scientific proc. style files, 2 figs., 4 page
Cosmic Topology: a Brief Overview
Questions such as whether we live in a spatially finite universe, and what
its shape and size may be, are among the fundamental open problems that high
precision modern cosmology needs to resolve. These questions go beyond the
scope of general relativity (GR), since as a (local) metrical theory GR leaves
the global topology of the universe undetermined. Despite our present-day
inability to predict the topology of the universe, given the wealth of
increasingly accurate astro-cosmological observations it is expected that we
should be able to detect it. An overview of basic features of cosmic topology,
the main methods for its detection, and observational constraints on
detectability are briefly presented. Recent theoretical and observational
results related to cosmic topology are also discussed.Comment: Revtex4, 9 pages, 2 figures. Ivited talk delivered at "XIV National
Meeting of the Brazilian Physical Society, section Particles and Fields,
Caxambu - MG, Brazil, from September 30 to October 04, 200
Determining the shape of the Universe using discrete sources
Suppose we have identified three clusters of galaxies as being topological
copies of the same object. How does this information constrain the possible
models for the shape of our Universe? It is shown here that, if the Universe
has flat spatial sections, these multiple images can be accommodated within any
of the six classes of compact orientable 3-dimensional flat space forms.
Moreover, the discovery of two more triples of multiple images in the
neighbourhood of the first one, would allow the determination of the topology
of the Universe, and in most cases the determination of its size.Comment: 11 pages, no figure