12,440 research outputs found
CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions
CMB anisotropy measurements have brought the issue of global topology of the
universe from the realm of theoretical possibility to within the grasp of
observations. The global topology of the universe modifies the correlation
properties of cosmic fields. In particular, strong correlations are predicted
in CMB anisotropy patterns on the largest observable scales if the size of the
Universe is comparable to the distance to the CMB last scattering surface. We
describe in detail our completely general scheme using a regularized method of
images for calculating such correlation functions in models with nontrivial
topology, and apply it to the computationally challenging compact hyperbolic
spaces. Our procedure directly sums over images within a specified radius,
ideally many times the diameter of the space, effectively treats more distant
images in a continuous approximation, and uses Cesaro resummation to further
sharpen the results. At all levels of approximation the symmetries of the space
are preserved in the correlation function. This new technique eliminates the
need for the difficult task of spatial eigenmode decomposition on these spaces.
Although the eigenspectrum can be obtained by this method if desired, at a
given level of approximation the correlation functions are more accurately
determined. We use the 3-torus example to demonstrate that the method works
very well. We apply it to power spectrum as well as correlation function
evaluations in a number of compact hyperbolic (CH) spaces. Application to the
computation of CMB anisotropy correlations on CH spaces, and the observational
constraints following from them, are given in a companion paper.Comment: 27 pages, Latex, 11 figures, submitted to Phys. Rev. D, March 11,
199
Surface networks
© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou
How the Universe got its Spots
The universe displays a three-dimensional pattern of hot and cold spots in
the radiation remnant from the big bang. The global geometry of the universe
can be revealed in the spatial distribution of these spots. In a topologically
compact universe, distinctive patterns are especially prominent in spatial
correlations of the radiation temperature. Whereas these patterns are usually
washed out in statistical averages, we propose a scheme which uses the
universe's spots to observe global geometry in a manner analogous to the use of
multiple images of a gravitationally lensed quasar to study the geometry of the
lens. To demonstrate how the geometry of space forms patterns in observations
of the microwave sky, we develop a simple real-space approximation to estimate
temperature correlations for any set of cosmological parameters and any global
geometry. We present correlated spheres which clearly show geometric pattern
formation for compact flat universes as well as for the compact negatively
curved space introduced by Weeks and another discovered by Best. These examples
illustrate how future satellite-based observations of the microwave background
can determine the full geometry of the universe.Comment: 16 pages, 26 figure
- …