The cosmic background radiation observed peaks at 160.2 GHz corresponding to wavelength 1.063 mm. The frequency for the electron corresponds to wavelength 1.23 nm for which the frequency is higher than CBR. Since using the Lawn-Roth analysis a hypersurface of the 4-sphere carrying eigenspinors satisfying and can be isometrically immersed into a 4-sphere of radius with mean curvature , we make the identification of the CBR frequency with the mean curvature of the physical universe. This is a reasonable thing to do because the the CBR can be considered universal and not isolated in some small subspace in the physical universe. The mean curvature is then simply the frequency assumed to be an integer as and the scaling for ensures that the eigenvalues of Dirac are integer multiples of . Note that matter in the universe is relatively sparse compared to the the background radiation. We can thus make the assumption that the physical universe is approximated by a constant mean curvature hypersurface of . We now apply the Alencar-do Carmo characterization of constant mean curvature hypersurfaces and find something interesting about the topology of the physical universe that consists only of CBR: it is an -torus. This is an interesting conclusion for it is not topologically the same as a 3-sphere. Here is the paper of Alencar-do Carmo: AlencarDoCarmoConstantMeanCurvature

## The shape of the physical universe with CBR is not a 3-sphere

May 7, 2014 by zulfahmed

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