1,099 research outputs found
Computing CMB Anisotropy in Compact Hyperbolic Spaces
The measurements of CMB anisotropy have opened up a window for probing the
global topology of the universe on length scales comparable to and beyond the
Hubble radius. For compact topologies, the two main effects on the CMB are: (1)
the breaking of statistical isotropy in characteristic patterns determined by
the photon geodesic structure of the manifold and (2) an infrared cutoff in the
power spectrum of perturbations imposed by the finite spatial extent. We
present a completely general scheme using the regularized method of images for
calculating CMB anisotropy in models with nontrivial topology, and apply it to
the computationally challenging compact hyperbolic topologies. This new
technique eliminates the need for the difficult task of spatial eigenmode
decomposition on these spaces. We estimate a Bayesian probability for a
selection of models by confronting the theoretical pixel-pixel temperature
correlation function with the COBE-DMR data. Our results demonstrate that
strong constraints on compactness arise: if the universe is small compared to
the `horizon' size, correlations appear in the maps that are irreconcilable
with the observations. If the universe is of comparable size, the likelihood
function is very dependent upon orientation of the manifold wrt the sky. While
most orientations may be strongly ruled out, it sometimes happens that for a
specific orientation the predicted correlation patterns are preferred over the
conventional infinite models.Comment: 15 pages, LaTeX (IOP style included), 3 color figures (GIF) in
separate files. Minor revision to match the version accepted in Class.
Quantum Grav.: Proc. of Topology and Cosmology, Cleveland, 1997. The paper
can be also downloaded from
http://www.cita.utoronto.ca/~pogosyan/cwru_proc.ps.g
The Coupling of Topology and Inflation in Noncommutative Cosmology
We show that, in a model of modified gravity based on the spectral action functional, there is a nontrivial coupling between cosmic topology and inflation, in the sense that the shape of the possible slow-roll inflation potentials obtained in the model from the nonperturbative form of the spectral action is sensitive not only to the geometry (flat or positively curved) of the universe, but also to the different possible non-simply connected topologies. We show this by explicitly computing the nonperturbative spectral action for some candidate flat cosmic topologies given by Bieberbach manifolds and showing that the resulting inflation potential differs from that of the flat torus by a multiplicative factor, similarly to what happens in the case of the spectral action of the spherical forms in relation to the case of the 3-sphere. We then show that, while the slow-roll parameters differ between the spherical and flat manifolds but do not distinguish different topologies within each class, the power spectra detect the different scalings of the slow-roll potential and therefore distinguish between the various topologies, both in the spherical and in the flat case
Black Hole Final State Conspiracies
The principle that unitarity must be preserved in all processes, no matter
how exotic, has led to deep insights into boundary conditions in cosmology and
black hole theory. In the case of black hole evaporation, Horowitz and
Maldacena were led to propose that unitarity preservation can be understood in
terms of a restriction imposed on the wave function at the singularity.
Gottesman and Preskill showed that this natural idea only works if one
postulates the presence of "conspiracies" between systems just inside the event
horizon and states at much later times, near the singularity. We argue that
some AdS black holes have unusual internal thermodynamics, and that this may
permit the required "conspiracies" if real black holes are described by some
kind of sum over all AdS black holes having the same entropy.Comment: Various minor improvements, references added, 25 page
A note on the 3D Ising model as a string theory
It has long been argued that the continuum limit of the 3D Ising model is
equivalent to a string theory. Unfortunately, in the usual starting point for
this equivalence -- a certain lattice theory of surfaces -- it is not at all
obvious how to take the continuum limit. In this note, I reformulate the
lattice theory of surfaces in a fashion such that the continuum limit is
straightforward. I go on to discuss how this new formulation may overcome some
fundamental objections to the notion that the Ising model is equivalent to a
string theory. In an appendix, I also discuss some aspects of fermion doubling,
and the lattice fermion formulation of the 2D Ising model.Comment: 21 pages, 11 figures. This revised manuscript is identical to the
final published version (Nuclear Physics B, to appear). Aside from correcting
some scattered typos, the final version corrects and expands some of the
comments in the original preprint on the unoriented NSR strin
The Implementation, Interpretation, and Justification of Likelihoods in Cosmology
I discuss the formal implementation, interpretation, and justification of likelihood attributions in cosmology. I show that likelihood arguments in cosmology suffer from significant conceptual and formal problems that undermine their applicability in this context
Topology and the Cosmic Microwave Background
Nature abhors an infinity. The limits of general relativity are often
signaled by infinities: infinite curvature as in the center of a black hole,
the infinite energy of the singular big bang. We might be inclined to add an
infinite universe to the list of intolerable infinities. Theories that move
beyond general relativity naturally treat space as finite. In this review we
discuss the mathematics of finite spaces and our aspirations to observe the
finite extent of the universe in the cosmic background radiation.Comment: Hilarioulsy forgot to remove comments to myself in previous version.
Reference added. Submitted to Physics Report
Black Strings, Black Rings and State-space Manifold
State-space geometry is considered, for diverse three and four parameter
non-spherical horizon rotating black brane configurations, in string theory and
-theory. We have explicitly examined the case of unit Kaluza-Klein momentum
black strings, circular strings, small black rings and black
supertubes. An investigation of the state-space pair correlation functions
shows that there exist two classes of brane statistical configurations, {\it
viz.}, the first category divulges a degenerate intrinsic equilibrium basis,
while the second yields a non-degenerate, curved, intrinsic Riemannian
geometry. Specifically, the solutions with finitely many branes expose that the
two charged rotating black strings and three charged rotating small
black rings consort real degenerate state-space manifolds. Interestingly,
arbitrary valued -dipole charged rotating circular strings and Maldacena
Strominger Witten black rings exhibit non-degenerate, positively curved,
comprehensively regular state-space configurations. Furthermore, the
state-space geometry of single bubbled rings admits a well-defined, positive
definite, everywhere regular and curved intrinsic Riemannian manifold; except
for the two finite values of conserved electric charge. We also discuss the
implication and potential significance of this work for the physics of black
holes in string theory.Comment: 41 pages, Keywords: Rotating Black Branes; Microscopic
Configurations; State-space Geometry, PACS numbers: 04.70.-s Physics of black
holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum aspects of black
holes, evaporation, thermodynamic
Collective Relaxation Dynamics of Small-World Networks
Complex networks exhibit a wide range of collective dynamic phenomena,
including synchronization, diffusion, relaxation, and coordination processes.
Their asymptotic dynamics is generically characterized by the local Jacobian,
graph Laplacian or a similar linear operator. The structure of networks with
regular, small-world and random connectivities are reasonably well understood,
but their collective dynamical properties remain largely unknown. Here we
present a two-stage mean-field theory to derive analytic expressions for
network spectra. A single formula covers the spectrum from regular via
small-world to strongly randomized topologies in Watts-Strogatz networks,
explaining the simultaneous dependencies on network size N, average degree k
and topological randomness q. We present simplified analytic predictions for
the second largest and smallest eigenvalue, and numerical checks confirm our
theoretical predictions for zero, small and moderate topological randomness q,
including the entire small-world regime. For large q of the order of one, we
apply standard random matrix theory thereby overarching the full range from
regular to randomized network topologies. These results may contribute to our
analytic and mechanistic understanding of collective relaxation phenomena of
network dynamical systems.Comment: 12 pages, 10 figures, published in PR
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