'Circles in the Sky' in twisted cylinders

It is shown here how prior estimates on the local shape of the universe can be used to reduce, to a small region, the full parameter space for the search of circles in the sky. This is the first step towards the development of efficientestrategies to look for these matched circles in order to detect a possible nontrivial topology of our Universe. It is shown how to calculate the unique point, in the parameter space, representing a pair of matched circles corresponding to a given isometry g (and its inverse). As a consequence, (i) given some fine estimates of the covering group of the spatial section of our universe, it is possible to confine, in a very effective way, the region of the parameter space in which to perform the searches for matched circles, and reciprocally (ii) once identified such pairs of matched circles, one could determine with greater precision the topology of our Universe and our location within it. It has recently been suggested that the quadrupole and octopole moments of the CMB anisotropies are almost aligned, i.e. each multipole has a preferred axis along which power is suppressed and both axes almost coincide. In fact, the angle between the preferred directions of these lowest multipoles is ∼10 ◦ , while the probability of this occurrence for two randomly oriented axes is roughly 1/62. There is also at present almost no doubt that the extremely low value of the CMB quadrupole is a real effect, i.e. it is not an illusion created by foregrounds