On Determining the Topology of the Observable Universe via 3-D Quasar Positions

Hot big bang cosmology says nothing about the topology of the Universe. A topology-independent algorithm is presented which is complementary to that of Lehoucq et al. 1996 and which searches for evidence of multi-connectedness using catalogues of astrophysically observed objects. The basis of this algorithm is simply to search for a quintuplet of quasars (over a region of a few hundred comoving Mpc) which can be seen in two different parts of our past time cone, allowing for a translation, an arbitrary rotation and possibly a reflection. This algorithm is demonstrated by application to the distribution of quasars between redshifts of $z=1$ and $z\approx4,$ i.e., at a comoving distance from the observer $1700 h^{-1}\mbox{\rm Mpc} \ltapprox d \ltapprox 3300 h^{-1}\mbox{\rm Mpc}.$ Two pairs of isometric quintuplets separated by more than {$300$\hMpc} are found. This is consistent with the number expected from Monte Carlo simulations in a simply connected Universe if the detailed anisotropy of sky coverage by the individual quasar surveys is taken into account. The linear transformation in (flat) comoving space from one quintuplet to another requires translations of {$353$\hMpc} and {4922\hMpc} respectively, plus a reflection in the former case, and plus both a rotation and a reflection in the latter. Since reflections are required, if these two matches were due to multi-connectedness, then the Universe would be non-orientable.