The study of topology of the universe using multipole vectors

We studied possibility of application of the multipole vectors decomposition of the cosmic microwave background (CMB) maps for detection signatures of non-trivial topology of the universe. Using 10 simulations we analysed distribution of the multipole vectors on the sky for the low order multipoles and probability distribution function of the statistics based on the sum of the dot products of the multipole vectors for the simply-connected flat universe as well universes with topology of a 3-torus. The estimated probabilities of obtaining values of the statistics at most as extreme as for the 5 years WMAP data shows that the observed alignment of the quadrupole and octopole slightly better fits to the universes with the 3-torus topology, where at least one the size of the fundamental domain is significantly shorter than the diameter of observable universe, rather than to simply-connected universe. However, any of the obtained results do not clearly rule out the latter (at most 94% confidence level). Nevertheless, the multipole vectors statistics appeared to not be very sensitive to the signatures of topology if the shorter size of the domain is comparable to the diameter of observable universe. The signatures are also significantly diluted by the integrated Sachs-Wolfe effect.