Void Sizes and CMBR Fluctuations

Following Blumenthal \etl \cite{blu} and Piran \etl \cite{Pi} I discuss a simple model for the gravitational formation of voids. This model enables us to estimate the primordial perturbation required on the scale of voids. A comparison of this condition with the constraints on the spectrum of fluctuations derived from CMBR observations reveals that gravitational growth of large voids require more power on the scale of $\approx 1500$\kms than is generally accepted in CDM models. For a generic power law primordial spectrum $P(k) \propto k^n$ gravitational growth of voids requires $n \gsim 1.25$, which is marginally compatible with the observed CMBR fluctuations. If future measurements will show that the amplitude of fluctuations required to produce the voids is too large they will imply that the voids did not grow gravitationally and that galaxies do not trace matter on very large scale.