## 1. IntroductionThe detection (Smoot et al. 1992; Bennett et al. 1994) and further
confirmation (Bennett et al. 1996; Hancock et al. 1994; Ganga et al.
1993) of the presence of anisotropies in the cosmic microwave
background (CMB), has endowed cosmologists with a unique tool for a
realistic test of cosmological models. The observed large angle
can be produced by a number of sources that go
from local, to astrophysical, to cosmological effects, among which the
most relevant are: emission from the Galaxy; gravitational
fluctuations produced by voids and great attractors; the Doppler
effect due to the observer's motion relative to the CMB; mixing of
geodesic flow; gravitational waves; cosmic strings; and gravitational
potential fluctuations on the last scattering surface - the
Sachs-Wolfe effect (for a review see White, Scott & Silk 1994).
Clearly the complexity of determining the cause of CMB anisotropies
requires several independent analysis techniques. Aside from the
standard statistical tests based on the angular auto-correlation
function and power spectrum, a number of statistics have been proposed
(Sazhin 1985; Vittorio & Juszkiewicz 1987; Bond & Efstathiou
1987; Coles 1988; Gott et al. 1990; Martínez-González
& Cayón 1992; Martínez-González & Sanz
1989) as topological descriptors to characterize the observed
anisotropies: hot spot number density, length and total curvature or
The great potential of topological analysis of CMB data can be
attested by the large number of results obtained thus far: the
We propose to use a topological analysis, based on the eccentricity or elongation measure of hot spots, to look for the signature of the mixing of geodesics effect (Gurzadyan & Kocharyan 1991, 1992). Because of the appealing possibility of extracting information about the curvature of the universe from the latter effect, we will deal with it in some detail. A consequence of mixing phenomena in geodesics propagation is the appearance of highly distorted anisotropy spots in cosmic background maps (Gurzadyan & Kocharyan 1993a, 1993b). In the case of an open geometry, anisotropy spots associated with a bundle of photons propagating in free space would appear as highly elongated hot spots, while in a flat space hot spots would show a symmetric circular shape. This visible effect is a direct consequence of the geometry of space and as such it is a unique tool to discriminate between open and closed cosmological models. However, confusion due to galactic contamination at high latitudes and similar elongated patterns produced by instrumental noise and cosmological structure characterized by large coherence angles makes this effect very difficult to observe. Fortunately, at least 3 different phenomena produced by the effect of mixing geodesics and associated with the observable characteristics of CMB, have been predicted: (a) (b) (c) In this paper we will deal only with the third phenomenon. Since, in principle, effects of apparent elongation might occur also owing to other physical mechanisms (the same is not excluded also for phenomena (a) and (b)), the unambiguous confirmation of the observational discovery of the effect of mixing geodesics could be reached by means of a comprehensive study of the complete set of predictions. As it is briefly discussed at the end of this paper, at least the available evidences do not contradict to all these predictions. A confirmation of the effect of mixing geodesics would constitute powerful probe of the curvature of the Universe. © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |