Constraints on the topology of the universe from the 2-yr COBE data

Angelica de Oliveira-Costa, George F. Smoot

Published 1994-12-01, updated 1997-05-14Version 2

The cosmic microwave background (CMB) is a unique probe of cosmological parameters and conditions. There is a connection between anisotropy in the CMB and the topology of the Universe. Adopting a universe with the topology of a 3-Torus, or a universe where only harmonics of the fundamental mode are allowed, and using 2-years of COBE/DMR data, we obtain constraints on the topology of the Universe. Previous work constrained the topology using the slope information and the correlation function of the CMB. We obtain more accurate results by using all multipole moments, avoiding approximations by computing their full covariance matrix. We obtain the best fit for a cubic toroidal universe of scale 7200h^{-1} Mpc for n=1. The data set a lower limit on the cell size of 4320h^{-1} Mpc at 95% confidence and 5880h^{-1} Mpc at 68% confidence. These results show that the most probable cell size would be around 1.2 times larger than the horizon scale, implying that the 3-Torus topology is no longer an interesting cosmological model.