Topology of the Universe from COBE-DMR -: a wavelet approach

In this paper, we pursue a new technique to search for evidence of a finite universe, making use of a spherical Mexican Hat wavelet decomposition of the microwave background fluctuations. Using the information provided by the wavelet coefficients at several scales, we test whether compact orientable flat topologies are consistent with the COBE-DMR data. We consider topological sizes ranging from half to twice the horizon size. A scale-scale correlation test indicates that non-trivial topologies with appropriate topological sizes are as consistent with the COBE-DMR data as an infinite universe. Among the finite models, the data seems to prefer a universe which is about the size of the horizon for all but the hypertorus and the triple-twist torus. For the latter, the wavelet technique does not seem a good discriminator of scales for the range of topological sizes considered here, while a hypertorus has a preferred size which is 80 per cent of the horizon. This analysis allows us to find a best fit topological size for each model, although cosmic variance might limit our ability to distinguish some of the topologies.