Analytic Formulae for the Off-Center CMB Anisotropy in a General Spherically Symmetric Universe

Abstract

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.