12 research outputs found
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
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
Topological Reverberations in Flat Space-times
We study the role played by multiply-connectedness in the time evolution of
the energy E(t) of a radiating system that lies in static flat space-time
manifolds M_4 whose t=const spacelike sections M_3 are compact in at least one
spatial direction. The radiation reaction equation of the radiating source is
derived for the case where M_3 has any non-trivial flat topology, and an exact
solution is obtained. We also show that when the spacelike sections are
multiply-connected flat 3-manifolds the energy E(t) exhibits a reverberation
pattern with discontinuities in the derivative of E(t) and a set of relative
minima and maxima, followed by a growth of E(t). It emerges from this result
that the compactness in at least one spatial direction of Minkowski space-time
is sufficient to induce this type of topological reverberation, making clear
that our radiating system is topologically fragile. An explicit solution of the
radiation reaction equation for the case where M_3 = R^2 x S^1 is discussed,
and graphs which reveal how the energy varies with the time are presented and
analyzed.Comment: 16 pages, 4 figures, REVTEX; Added five references and inserted
clarifying details. Version to appear in Int. J. Mod. Phys. A (2000
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
Signature for the Shape of the Universe
If the universe has a nontrivial shape (topology) the sky may show multiple
correlated images of cosmic objects. These correlations can be couched in terms
of distance correlations. We propose a statistical quantity which can be used
to reveal the topological signature of any Robertson-Walker (RW) spacetime with
nontrivial topology. We also show through computer-aided simulations how one
can extract the topological signatures of flat, elliptic, and hyperbolic RW
universes with nontrivial topology.Comment: 11 pages, 3 figures, LaTeX2e. This paper is a direct ancestor of
gr-qc/9911049, put in gr-qc archive to make it more accessibl
Casimir Effect in closed spaces
As it is well known the topology of space is not totally determined by
Einstein's equations. It is considered a massless scalar quantum field in a
static Euclidean space of dimension 3. The expectation value for the energy
density in all compact orientable Euclidean 3-spaces are obtained in this work
as a finite summation of Epstein type zeta functions. The Casimir energy
density for these particular manifolds is independent of the type of coupling
with curvature. A numerical plot of the result inside each Dirichlet region is
obtained.Comment: Version accepted for publication. The most general coupling with
curvature is chose
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
Radiation Damping in FRW Space-times with Different Topologies
We study the role played by the compactness and the degree of connectedness
in the time evolution of the energy of a radiating system in the
Friedmann-Robertson-Walker (FRW) space-times whose spacelike
sections are the Euclidean 3-manifold and six topologically
non-equivalent flat orientable compact multiply connected Riemannian
3-manifolds. An exponential damping of the energy is present in the
case, whereas for the six compact flat 3-spaces it is found
basically the same pattern for the evolution of the energy, namely relative
minima and maxima occurring at different times (depending on the degree of
connectedness) followed by a growth of . Likely reasons for this
divergent behavior of in these compact flat 3-manifolds are discussed
and further developments are indicated. A misinterpretation of Wolf's results
regarding one of the six orientable compact flat 3-manifolds is also indicated
and rectified.Comment: 13 pages, RevTeX, 5 figures, To appear in Phys. Rev. D 15, vol. 57
(1998