Sources of CMB Spots in Closed Hyperbolic Universes

Details Sources of CMB Spots in Closed Hyperbolic Universes Sources of CMB Spots in Closed Hyperbolic Universes

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet.1929f&link_type=abstract

"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R

Physics

Scientific paper

Some years ago Cayón and Smoot1; hereafter CS, identified a number of 'cold' and 'hot' spots in the COBE maps of the cosmic microwave background (CMB), as patches of physical density fluctuations (rather than noise) on the surface of last scattering (SLS). A cold (hot) spot, interpreted as gravitational Sachs-Wolfe effect plus fluctuation of radiation temperature on the SLS, corresponds to an increase (decrease) of matter density2. These results were used by the author3; henceforth Paper I, in connection with the possibility of the universe's spatial section being a closed hyperbolic 3-manifold (CHM).
In the electronic version of this paper Tables 1a-b list the galactic coordinates for the six overerdense and the eight underdense CS spots. Given the comoving nature of cosmic geometry, it was argued that those spots, for example the overdense ones, might have evolved into galaxy superclusters which are - or may become - observable in our epoch. The underdense spots would have evolved into the relative voids in the observed structure of the large-scale matter distribution.
The purpose of Paper I was to fit a number of CHM's to the CS spots. Since these are interpreted as density inhomogeneities in the fundamental polyhedron (FP) for the manifold, we hoped the positions of the latter, when compared with those of observed structures and voids, might favor some of those CHM's as the real cosmic space.
In Paper I a lopsided method was adopted to choose a possible source for a given CS spot. The sources obtained in Paper I are usually concentrated in narrow bands of galactic latitude. Another problem with Paper I was that we looked for sources inside the maximum injectivity FP, with basepoint at the center (which is the standard in SnapPea4) and the observer displaced from the center; this produces an asymmetry in the distances of the found candidate sources.
Here I make two improvements on this research, both with the help of our geometer guru, Jeff Weeks. One of them is that now FP is chosen with basepoint on the observer's position, which makes the source distribution centered on the the observer. The other one is in the search procedure.
The new computer search for P and γ is shown in the electronic paper as a flow chart. It is based on the very definition of a fundamental region. There the results for manifold m007(+3, 1) in the notation of SnapPea are shown. The observer was supposed to be at position (0.3, 0.0, 0.0) in Klein coordinates relative to the standard FP in SnapPea, and axes rotated by (4.5669, 0.1078, 5.3451) in Euler angles in radians, with respect to the axes obtained for the displaced basepoint. The values Ω0 = 0.3 and ZSLS = 1300 were adopted.
The idea to pursue, which is illustrated in Paper I, is to vary these positions and orientations randomly, until we get sources that match data in catalogs of galaxy superclusters and voids - which, for this to become possible, should reach much deeper space than the present limit of about Z = 0.12 in Einasto et al.'s5 list of superclusters.

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