The significance of the largest scale CMB fluctuations in WMAP
Constraining rectangular topologies with the COBE/DMR
Constraining cubic topologies with the COBE/DMR
We investigate anomalies reported in the Cosmic Microwave Background
maps from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite on
very large angular scales and discuss possible interpretations. Three
independent anomalies involve the quadrupole and octopole:
Despite
this, we still had the possibility of living in a universe with a more
anisotropic topology such as a rectangular T^3 small universe
with one or two of its dimensions significantly smaller than the present
horizon (which we refer to as T^1 and T^2 models, respectively).
In order to rule out these anisotropic topologies as well, we applied
a new data analysis method (the S-statistic) that searches for the
specific kind of symmetries that these models should produce. We found that
the 4 year COBE/DMR data set a lower limit on the smallest cell size for
T^1 and T^2 models of 3000h^(-1) Mpc, at 95% confidence,
for n = 1. In other words, these results (together with those described
above) imply that all toroidal universes (cubes and rectangles) are
also
ruled out as interesting cosmological models.
Using 2 years of COBE/DMR data, we computed the
expected anisotropies for a universe with topology T^3, and found
that this model is for all practical purposes
ruled out.
Previous work constrained the topology using power spectrum slope
information and the correlation function of the CMB. We obtained more accurate
results by using all multipole moments, avoiding approximations by computing
their full covariance matrix. We obtained the best fit for a cubic toroidal
universe of scale Lx = Ly = Lz = 7200h^(-1) Mpc for
n = 1. The data set a lower limit on the cell size of 4300h^(-1)
Mpc at 95%confidence and 5900h^(-1) Mpc at 68% confidence. In other
words, we showed that the cubic T^3 cell could not be much smaller
than the horizon scale, which rules it out as an interesting cosmological
model.
