LIMITS ON THE PRIMORDIAL FLUCTUATION SPECTRUM - VOID SIZES AND ANISOTROPY OF THE COSMIC MICROWAVE BACKGROUND-RADIATION

We suggest the use of the typical appearance of voids on a scale of 50 00 km s-1 in the galaxy distribution to estimate the power spectrum on this scale. We use a simple model for the gravitational formation of voids, and we compare the results with the matter fluctuations as cons trained by the CMBR observations by COBE. We find that a power spectru m P(k) is-proportional-to k(n) with n almost-equal-to 1.25 is compatib le both with COBE and with the gravitational growth of large voids in an OMEGA = 1 universe. A Harrison-Zel'dovich spectrum, n = 1, normaliz ed to produce the observed CMBR fluctuations, does not have enough pow er for gravitational growth of voids with a diameter of 5000 km s-1 in an OMEGA = 1 universe. Such a spectrum would be compatible if (i) voi d diameters were smaller (3500 km s-1), the voids were shallower or th e voids were rare (we assume that the Universe is void-filled), (ii) O MEGA < 1 (i.e. the Universe is open), (iii) galaxies do not trace matt er on very large scales, or (iv) the voids do not grow gravitationally .