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 \lambda _ { peak } proportional to the cutoff radius R _ { 0 } 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 R _ { 0 } = 35 \pm 12 h ^ { -1 } Mpc for the correlation length , and n = 0.76 \pm 0.3 for the spectral index of P ( k ) in the large wavelength region .
The inferred scale in the spectrum is \lambda _ { peak } = 51 \pm 18 h ^ { -1 } Mpc .
This number agrees with that derived from the analysis of the correlation function of matter and with a preferred scale identified in IRAS PSC .