COBE and Global Topology: An Example of the Application of the Identified Circles Principle

Abstract

The significance to which the cosmic microwave background observations by the satellite COBE can be used to refute a specific observationally based hypothesis for the global topology (3-manifold) of the Universe is investigated, by a new method of applying the principle of matched circle pairs. Moreover, it is shown that this can be done without assuming Gaussian distributions for the density perturbation spectrum. The Universe is assumed to correspond to a flat Friedmann-Lema\^{\i}tre model with a zero value of the cosmological constant. The 3-manifold is hypothesised to be a 2-torus in two directions, with a third axis larger than the horizon diameter. The positions and lengths of the axes are determined by the relative positions of the galaxy clusters Coma, RX~J1347.5-1145 and CL 09104+4109, assumed to be multiple topological images of a single, physical cluster. If the following two assumptions are valid: (i) the error estimates in the COBE DMR data are accurate estimates of the total random plus systematic error; and (ii) the temperature fluctuations are dominated by the na\"{\i}ve Sachs-Wolfe effect; then the distribution of the temperature differences between multiply imaged pixels is significantly wider than the uncertainty in the differences, and the candidate is rejected at the 94% level. This result is valid for either the `subtracted' or `combined' Analysed Science Data Sets, for either $10\deg$ or $20\deg$ smoothing, and is strengthened if suspected contaminated regions from the galactic centre and the Ophiuchus and Orion complexes are removed.