The power spectrum implied by COBE and the matter correlation function

A phenomenological power spectrum of primordial density perturbations has been constructed by using both COBE data to probe the large wavelength region, and a double power law, locally deduced from galaxy catalogs, which describes the matter correlation function up to tens of Megaparsec. The shape of the spectrum P(k) of density fluctuations exhibits a peak that singles out a characteristic wavelength proportional to the cutoff radius R0 in the matter distribution (comparable to the distance at which matter becomes anticorrelated). {}From a least squares fit to COBE's angular correlation function we obtain R0 = 35 +- 12 Mpc/h for the correlation length, and n = 0.76 +- 0.3 for the spectral index of P(k) in the large wavelength region. The inferred scale in the spectrum is 51 +- 18 Mpc/h. This number agrees with that derived from the analysis of the correlation function of matter and with a preferred scale identified in IRAS PSC.