Statistics of the microwave background anisotropies caused by squeezed cosmological perturbations

Abstract

It is likely that the observed large-angular-scale anisotropies in the microwave background radiation are induced by cosmological perturbations of quantum-mechanical origin. Such perturbations are now placed in squeezed vacuum quantum states and, hence, are characterized by large variances of their amplitude. The statistical properties of the anisotropies should reflect the underlying statistics of the squeezed vacuum quantum states. The theoretical variances for the temperature angular correlation function are derived and described quantitatively. It is shown that they are indeed large and must be present in observational data if the anisotropies are truly caused by perturbations of quantum-mechanical origin. Unfortunately, these large theoretical statistical uncertainties will make the extraction of cosmological information from the measured anisotropies a much more difficult problem than we wanted it to be. © 1996 The American Physical Society.