An analytical approach to the CMB Polarization in a Spatially Closed
  background
  The scalar mode polarization of the cosmic microwave background is derived in
a spatially closed universe from the Boltzmann equation using the line of sight
integral method. The EE and TE multipole coefficients have been extracted
analytically by considering some tolerable approximations such as considering
the evolution of perturbation hydrodynamically and sudden transition from
opacity to transparency at the time of last scattering. As the major advantage
of analytic expressions, EE and TE multipole coefficients explicitly show the
dependencies on baryon density, matter density, curvature, primordial spectral
index, primordial power spectrum amplitude, Optical depth, recombination width
and recombination time. Using a realistic set of cosmological parameters taken
from a fit to data from Planck, the closed universe EE and TE power spectrums
in the scalar mode are compared with numerical results from the CAMB code and
also latest observational data. The analytic results agree with the numerical
ones on the big and moderate scales. The peak positions are in good agreement
with the numerical result on these scales while the peak heights agree with
that to within 20% due to the approximations have been considered for these
derivations. Also, several interesting properties of CMB polarization are
revealed by the analytic spectra.
