The angular power spectrum of the four-year COBE data

The angular power spectrum C-l is extracted from the 4 yr COBE Differential Microwave Radiometer (DMR) data with a 20 degrees Galactic cut, using the narrowest window functions possible. The average power in eight multipole bands is also computed and plotted together with a compilation of power spectrum measurements from other experiments. The COBE results are found to be consistent with an n = 1 power spectrum with the normalization Q(rms,ps) = 18 mu K reported by the COBE DMR team. Certain nonstandard cosmologies, such as ''small universe'' models with nontrivial spatial topology, predict power spectra that are not smooth functions. Rather, they contain bumps and wiggles that may not have been detected by other data analysis techniques such as the Hauser-Peebles method, the band-power method, and orthogonalized spherical harmonics, since these methods all give broader window functions that can smear such features out beyond recognition. On the large angular scales probed by COBE, the universe thus appears to be kind to us, presenting a power spectrum that is a simple smooth function.