Constraining cosmological topology via highly luminous X-ray clusters

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Abstract
The topology of the observable Universe is not yet known. The most significant observational sign of a non-trivial topology would be multiple images (‘ghosts’) of a single object at (in general) different sky positions and redshifts. It is pointed out that the previous search by Gott for ghost images of the Coma cluster can be extended by using highly X-ray-luminous clusters of galaxies. This is likely to be more efficient than with other astrophysical objects viewable on these scales, since (1) X-ray clusters would be at least as easy to identify if viewed from other angles as any other objects, and (2) the evolution of the X-ray-emitting, thermally heated gas is likely to be simpler than for other objects. Possibilities that the highly luminous cluster RX J1347.5-1145 (z = 0.45) has a ‘ghost image’ at lower redshift are analysed. It is noted that RX J1347.5 —1145, the Coma cluster and the cluster CL 09104 + 4109 form nearly a right angle ( ≈88°) with arms of nearly identical length (970 and 960 h−1 Mpc respectively) for Ω0 = 1, λ0 = 0 curvature (h=H0 100 km s−1 Mpc−1). This is a clue that the three clusters could be ghost images of one and the same cluster, for a hypertoroidal T3. topology. However, several arguments are presented that this relation is not physical.
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