255 research outputs found
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
Generalized Chaplygin gas model, supernovae and cosmic topology
In this work we study to which extent the knowledge of spatial topology may
place constraints on the parameters of the generalized Chaplygin gas (GCG)
model for unification of dark energy and dark matter. By using both the
Poincar\'e dodecahedral and binary octahedral spaces as the observable spatial
topologies, we examine the current type Ia supernovae (SNe Ia) constraints on
the GCG model parameters. We show that the knowledge of spatial topology does
provide additional constraints on the parameter of the GCG model but does
not lift the degeneracy of the parameter.Comment: Revtex 4, 8 pages, 10 figures, 1 table; version to match the
published on
Low-lying fermion modes of Nf=2 improved Wilson fermions
We present preliminary results for the topological charge and susceptibility
determined from the low-lying eigenmodes of the Wilson-Dirac operator. These
modes have been computed on dynamical configurations with Nf=2
non-perturbatively improved Wilson fermions. We compare our results with the
eigenmodes of fermions in the quenched approximation.Comment: Lattice2001(confinement), 3 pages, 5 Figure
Observational constraints on modified gravity models and the Poincar\'e dodecahedral topology
We study the constraints that spatial topology may place on the parameters of
models that account for the accelerated expansion of the universe via infrared
modifications to general relativity, namely the Dvali-Gabadadze-Porrati
braneworld model as well as the Dvali-Turner and Cardassian models. By
considering the Poincar\'e dodecahedral space as the circles-in-the-sky
observable spatial topology, we examine the constraints that can be placed on
the parameters of each model using type Ia supernovae data together with the
baryon acoustic peak in the large scale correlation function of the Sloan
Digital Sky Survey of luminous red galaxies and the Cosmic Microwave Background
Radiation shift parameter data. We show that knowledge of spatial topology does
provide relevant constraints, particularly on the curvature parameter, for all
models.Comment: Revtex4, 10 pages, 1 table, 12 figures; version to match the one to
be published in Physical Review
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
Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement
Exact-diagonalization calculations for N=3 electrons in anisotropic quantum
dots, covering a broad range of confinement anisotropies and strength of
inter-electron repulsion, are presented for zero and low magnetic fields. The
excitation spectra are analyzed as a function of the strength of the magnetic
field and for increasing quantum-dot anisotropy. Analysis of the intrinsic
structure of the many-body wave functions through spin-resolved two-point
correlations reveals that the electrons tend to localize forming Wigner
molecules. For certain ranges of dot parameters (mainly at strong anisotropy),
the Wigner molecules acquire a linear geometry, and the associated wave
functions with a spin projection S_z=1/2 are similar to the representative
class of strongly entangled states referred to as W-states. For other ranges of
parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a
more complex structure consisting of two mirror isosceles triangles. This
latter structure can be viewed as an embryonic unit of a zig-zag Wigner crystal
in quantum wires. The degree of entanglement in three-electron quantum dots can
be quantified through the use of the von Neumann entropy.Comment: To appear in Physical Review B. REVTEX4. 13 pages with 16 color
figures. To download a copy with higher-quality figures, go to publication
#78 in http://www.prism.gatech.edu/~ph274cy
Single polaron properties of the breathing-mode Hamiltonian
We investigate numerically various properties of the one-dimensional (1D)
breathing-mode polaron. We use an extension of a variational scheme to compute
the energies and wave-functions of the two lowest-energy eigenstates for any
momentum, as well as a scheme to compute directly the polaron Greens function.
We contrast these results with results for the 1D Holstein polaron. In
particular, we find that the crossover from a large to a small polaron is
significantly sharper. Unlike for the Holstein model, at moderate and large
couplings the breathing-mode polaron dispersion has non-monotonic dependence on
the polaron momentum k. Neither of these aspects is revealed by a previous
study based on the self-consistent Born approximation
Symmetries of hadrons after unbreaking the chiral symmetry
We study hadron correlators upon artificial restoration of the spontaneously
broken chiral symmetry. In a dynamical lattice simulation we remove the lowest
lying eigenmodes of the Dirac operator from the valence quark propagators and
study evolution of the hadron masses obtained. All mesons and baryons in our
study, except for a pion, survive unbreaking the chiral symmetry and their
exponential decay signals become essentially better. From the analysis of the
observed spectroscopic patterns we conclude that confinement still persists
while the chiral symmetry is restored. All hadrons fall into different chiral
multiplets. The broken U(1)_A symmetry does not get restored upon unbreaking
the chiral symmetry. We also observe signals of some higher symmetry that
includes chiral symmetry as a subgroup. Finally, from comparison of the \Delta
- N splitting before and after unbreaking of the chiral symmetry we conclude
that both the color-magnetic and the flavor-spin quark-quark interactions are
of equal importance.Comment: 12 pages, 14 figures; final versio
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
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