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The Cosmological Principle postulates that the Universe is homogeneous and isotropic about us (located at the origin). The proper distance R LSS to the last scattering surface (LSS), and the blackbody temperature T(z LSS) at that redshift, should thus be independent of direction. The CMB originates from a spherical shell at R LSS (we ignore the actualy thickness of the emission region, which is much smaller than R LSS), and propagates towards us through an optically thin medium. For simplicity, we assume the Universe is completely opaque beyond the LSS.
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The Universe appears to have a 'preferred' frame of reference, within which the cosmic microwave background is completely isotropic. Earth's motion through this relic radiation field is measurable, and some have viewed this type of observation as a possible contradiction of Einstein's principle of relativity. Several experiments have been proposed...
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