The Topology and Size of the Universe from CMB Temperature and
  Polarization Data
  We analyze seven year and nine year WMAP temperature maps for signatures of
three finite flat topologies M_0=T^3, M_1=T^2 x R^1, and M_2=S^1 x R^2. We use
Monte-Carlo simulations with the Feldman-Cousins method to obtain confidence
intervals for the size of the topologies considered. We analyze the V, W, and Q
frequency bands along with the ILC map and find no significant difference in
the results. The 95.5% confidence level lower bound on the size of the topology
is 1.5L_0 for M_0, 1.4L_0 for M_1, and 1.1L_0 for M_2, where L_0 is the radius
of the last scattering surface. Our results agree very well with the recently
released results from the Planck temperature data. We show that the likelihood
function is not Gaussian in the size, and therefore simulations are important
for obtaining accurate bounds on the size. We then introduce the formalism for
including polarization data in the analysis. The improvement that we find from
WMAP polarization maps is small because of the high level of instrumental
noise, but our forecast for Planck maps shows a much better improvement on the
lower bound for L. For the M_0 topology we expect an improvement on the lower
bound of L from 1.7L_0 to 1.9L_0 at 95.5% confidence level. Using both
polarization and temperature data is important because it tests the hypothesis
that deviations in the TT spectrum at small l originate in the primordial
perturbation spectrum.
