Testing the effect of geodesic mixing with COBE data to Reveal the Curvature of the Universe

Abstract

When considering the statistical properties of a bundle of cosmic microwave background (CMB) photons propagating through space, the effect of `mixing geodesics' appears with a distinct signature that depends on the geometry of space. In a Universe with negative curvature this effect is expected to produce elongated anisotropy spots on CMB maps. We used COBE-DMR data to look for such effect. Based on the analysis of a measure of eccentricity of hot spots it appears that there is a clear indication of an excess eccentricity of hot spots with respect to that expected from noise alone. This result must be interpreted with caution as this effect can be due in part to galactic emission. If the detected eccentricity of anisotropy spots can be attributed to the effect of mixing it implies the negative curvature of the Universe and a value of $\Omega < 1$.