Scale-Invariant Spectrum of Cosmic Background Radiation as a Feature of the Universe with Negative Curvature

Abstract

As was shown before (Gurzadyan and Kocharyan, 1992, 1993ab) the statistical properties (exponential mixing) of motion of CMB photon beams in Friedmann Universe with negative curvature can have definite observable consequences including the decrease of the CMB anisotropy amplitude after the last scattering, distortion of images on CMB sky maps. Here we consider one more consequence concerning the behaviour of temperature autocorrelation function C(\theta,\beta), where \theta is the modulation (separation) angle, and \beta the observing beam effective angle. We prove that in the Universe with negative curvature any spectrum of perturbations at last scattering epoch becomes a scale-invariant by present time. It is also predicted that the temperature autocorrelation function should increase while obtained from measurements with small beam sizes within some mixing beam angle.