ANISOTROPY OF COSMIC BACKGROUND-RADIATION FROM A SPHERICAL CLUSTERING ON LARGE SCALES

We present an exact frequency shift of a photon passing through a spherically symmetric collapsing in a flat and pressureless universe. This model can be used to study the temperature distortion of cosmic background radiation (CBR) caused by density perturbations lying on the range from last scattering to the vicinity of observer. The dependencies of CBR temperature fluctuations on the density contrast, the spatial and/or angular size, and the location of the initially spherically perturbed region have been investigated. We found that the signature of the temperature distortion sensitively depends on the density profile and location of the perturbed region. It also showed that the CBR temperature anisotropy on scales greater-than-or-equal-to 5-degrees would be dominated by large-scale clustering occurring after decoupling, not by the perturbations at the last scattering. Therefore, CBR anisotropies on intermediate and larger angular scales are not only dependent on density and potential structures at the epoch of decoupling and the relevant horizon, but also on the structure formation occurring in the post-decoupling era. If the recent COBE observation on CBR anisotropy at a scale of 10-degrees is caused by such large-scale clustering, the corresponding initial density fluctuation on the comoving spatial scale of 1000 h-1 Mpc is found to be 2.8 x 10(-6) and 6.9 x 10(-6) for the perburbed regions located on the last scattering surface and at redshift approximately 100, respectively. By using the developed mechanism, the CBR dipole anisotropy can also set an effective constraint on the initial density constrast.