3,807 research outputs found
Holographic Thermodynamic on the Brane in Topological Reissner-Nordstr\"om de Sitter Space
We consider the brane universe in the bulk background of the topological
Reissner-Nordstr\"om de Sitter black holes. We show that the thermodynamic
quantities (including entropy) of the dual CFT take usual special forms
expressed in terms of Hubble parameter and its time derivative at the moment,
when the brane crosses the black hole horizon or the cosmological horizon. We
obtain the generalized Cardy-Verlinde formula for the CFT with an charge and
cosmological constant, for any values of the curvature parameter in the
Friedmann equations.Comment: 8 page
Deconstructing de Sitter
Semiclassical gravity predicts that de Sitter space has a finite entropy. We suggest a picture for Euclidean de Sitter space in string theory, and use the AdS/CFT correspondence to argue that de Sitter entropy can be understood as the number of degrees of freedom in a quantum mechanical dual
Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web
We study the topology of the Megaparsec Cosmic Web in terms of the
scale-dependent Betti numbers, which formalize the topological information
content of the cosmic mass distribution. While the Betti numbers do not fully
quantify topology, they extend the information beyond conventional cosmological
studies of topology in terms of genus and Euler characteristic. The richer
information content of Betti numbers goes along the availability of fast
algorithms to compute them.
For continuous density fields, we determine the scale-dependence of Betti
numbers by invoking the cosmologically familiar filtration of sublevel or
superlevel sets defined by density thresholds. For the discrete galaxy
distribution, however, the analysis is based on the alpha shapes of the
particles. These simplicial complexes constitute an ordered sequence of nested
subsets of the Delaunay tessellation, a filtration defined by the scale
parameter, . As they are homotopy equivalent to the sublevel sets of
the distance field, they are an excellent tool for assessing the topological
structure of a discrete point distribution. In order to develop an intuitive
understanding for the behavior of Betti numbers as a function of , and
their relation to the morphological patterns in the Cosmic Web, we first study
them within the context of simple heuristic Voronoi clustering models.
Subsequently, we address the topology of structures emerging in the standard
LCDM scenario and in cosmological scenarios with alternative dark energy
content. The evolution and scale-dependence of the Betti numbers is shown to
reflect the hierarchical evolution of the Cosmic Web and yields a promising
measure of cosmological parameters. We also discuss the expected Betti numbers
as a function of the density threshold for superlevel sets of a Gaussian random
field.Comment: 42 pages, 14 figure
What we don't know about time
String theory has transformed our understanding of geometry, topology and
spacetime. Thus, for this special issue of Foundations of Physics commemorating
"Forty Years of String Theory", it seems appropriate to step back and ask what
we do not understand. As I will discuss, time remains the least understood
concept in physical theory. While we have made significant progress in
understanding space, our understanding of time has not progressed much beyond
the level of a century ago when Einstein introduced the idea of space-time as a
combined entity. Thus, I will raise a series of open questions about time, and
will review some of the progress that has been made as a roadmap for the
future.Comment: 15 pages; Essay for a special issue of Foundations of Physics
commemorating "Forty years of string theory
Quasi-Fuchsian AdS representations are Anosov
In a recent paper, Q. M\'erigot proved that representations in SO(2,n) of
uniform lattices of SO(1,n) which are Anosov in the sense of Labourie are
quasi-Fuchsian, i.e. are faithfull, discrete, and preserve an acausal subset in
the boundary of anti-de Sitter space. In the present paper, we prove the
reverse implication. It also includes: -- A construction of Dirichlet domains
in the context of anti-de Sitter geometry, -- A proof that spatially compact
globally hyperbolic anti-de Sitter spacetimes with acausal limit set admit
locally CAT(-1) Cauchy hypersurfaces
String theory: an update
An overview of some of the developments in string theory over the past two
years is given, focusing on four topics: realistic (standard model like) models
from string theory, geometric engineering and theories with fluxes, the gauge
theory-gravity correspondence, and time dependent backgrounds and string
theory. Plenary talk at ICHEP'02, Amsterdam, July 24-31, 2002.Comment: 20 pages, 2 figures, uses espcrc2.sty, v2: several references added,
apologies for the delay in submitting this updated versio
dS/CFT Duality on the Brane with a Topological Twist
We consider a brane universe in an asymptotically de Sitter background
spacetime of arbitrary dimensionality. In particular, the bulk spacetime is
described by a ``topological de Sitter'' solution, which has recently been
investigated by Cai, Myung and Zhang. In the current study, we begin by showing
that the brane evolution is described by Friedmann-like equations for radiative
matter. Next, on the basis of the dS/CFT correspondence, we identify the
thermodynamic properties of the brane universe. We then demonstrate that many
(if not all) of the holographic aspects of analogous AdS-bulk scenarios
persist. These include a (generalized) Cardy-Verlinde form for the CFT entropy
and various coincidences when the brane crosses the cosmological horizon.Comment: 24 pages, Latex; references added and Section 5 enhance
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