OBSERVATIONAL CONSTRAINTS ON THE SPECTRAL INDEX

We address the possibility of bounding the spectral index n of primord ial density fluctuations, using both the cosmic microwave background ( cmb) anisotropy, which probes scales 10(3) to 10(4) Mpc, and data on g alaxies and clusters which probes scales 1 to 100 Mpc. Given n, suffic iently accurate large scale data on the cmb anisotropy can determine t he normalization of the primordial spectrum. Then the small scale data are predicted within a given model of structure formation, which we h ere lake as the MDM model determined by the Hubble parameter H-0 and t he neutrino fraction Omega(v). Each piece of small scale data is reduc ed to a value of sigma (R) (the linearly evolved rms density contrast with top hat smoothing on scale R) which allows data on different scal es to be readily compared. As a preliminary application, we normalize the spectrum using the ten degree variance of the COBE data, and then compare the prediction with a limited sample of low energy data, for v arious values of n, Omega(v) and H-0. With H-0 fixed at 50 kms(-1) Mpc (-1), the data constrain the spectral index to the range 0.7 less than or similar to n less than or similar to 1.2. If gravitational waves c ontribute to the cmb anisotropy with relative strength R = 6(1 - n) (a s in some models of inflation), the lower limit on n is increased to a bout 0.85. The uncertainty in H-0 widens this band by about 0.1 at eit her end.