The Angular Power Spectrum of the Four-Year [ITAL]COBE[/ITAL] Data

The angular power spectrum C_l is extracted from the 4 year COBE DMR datawith a 20 degree galactic cut, using the narrowest window functions possible.The average power in eight multipole bands is also computed, and plottedtogether with a compilation of power spectrum measurements from otherexperiments. The COBE results are found to be consistent with an n=1 powerspectrum with the normalization Qrmsps=18 microkelvin reported by the COBE DMRteam. Certain non-standard cosmologies, such as "small universe" models withnontrivial spatial topology, predict power spectra which are not smoothfunctions. Rather, they contain bumps and wiggles that may not have beendetected by other data analysis techniques such as the Hauser-Peebles method(Wright etal 1996), the band-power method (Hinshaw etal 1996) andorthogonalized spherical harmonics (Gorski etal 1996), since these methods allgive broader window functions that can smear such features out beyondrecognition. On the large angular scales probed by COBE, the Universe thusappears to be kind to us, presenting a power spectrum that is a simple smoothfunction.