Analytic formulae for the off-center CMB anisotropy in a general
  spherically symmetric universe
  The local void model has recently attracted considerable attention because it
can explain the apparent accelerated expansion of the present universe without
introducing dark energy. However, in order to justify this model as an
alternative to the standard $\Lambda$CDM cosmology, the model should be tested
by various observations, such as the CMB temperature anisotropy, besides the
distance-redshift relation of SNIa. For this purpose, we derive analytic
formulae for the dipole and quadrupole moments of the CMB temperature
anisotropy that hold for any spherically symmetric universe model and can be
used to compare consequences of such a model with observations of the CMB
temperature anisotropy rigorously. We check that our formulae are consistent
with the numerical studies previously made for the CMB temperature anisotropy
in the void model. We also update the constraints concerning the location of
the observers in the void model by applying our analytic dipole formula with
the latest WMAP data.
