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UBC Theses and Dissertations

On recent constraints for the minimum scale of a small compact universe with three-torus topology Lee, Henry


We have embarked upon simple tests to gauge the validity of assumptions made by Fang and Liu in their assessment of opposite quasar pairs as a probe of global topology in the universe. Constraints for the scale of a three-torus (T-3) universe obtained from searches of opposite pairs of quasars by Fang and Liu have been claimed as the strongest to date. However, two assumptions involved are shown to be invalid: quasar images are not distributed uniformly across the sky and the observer and the object within the fundamental cell are not coincident. So, detected images of the object are not located back-to-back. We perform two numerical calculations in a simulated survey. A three-dimensional computational lattice with unit volumes was arranged as the model for a small universe with three-torus topology. The first calculation sets coincident observer and object positions within the unit cell while the second calculation places the observer randomly within the unit cell. The computational lattice was surveyed with two by two degree square beams for images of the object and the number of opposite pairs of images was counted. Our results show that opposite pairs of quasars are detected infrequently and that the Fang and Liu limit is overestimated by a factor of ten in probability. To obtain their90% confidence in pair detection probability, their limit underestimates the number of toroidal diameters by a factor of two. Consequently, their claimed lower limit of 200Mpc for the minimum scale of a three-torus universe is reduced by two to 100 Mpc. The absence of many opposite quasar pairs does not constrain the minimum scale of a toroidal universe and any search for opposite quasar pairs is not a useful method to investigate the existence or constrain the size of a possible toroidal universe.

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