Fluctuations of the cosmic background radiation appearing in the 10-dimensional cosmological model

Abstract

We consider a cosmological model starting from (1) the (1 + 3 + 6)-dimensional space-times consisting of the outer space (the 3-dimensional expanding section) and the inner space (the 6-dimensional section) and reaching (2) the Friedmann model after the decoupling of the outer space from the inner space, and derive fluctuations of the background radiation appearing in the above 10-dimensional space-times. For this purpose we first derive the fluid-dynamical perturbations in the above 10-dimensional space-times, corresponding to two kinds of curvature perturbations (in the scalar mode) in the non-viscous case, and next study the quantum fluctuations in the scalar and tensor modes, appearing at the stage when the perturbations are within the horizon of the inflating outer space. Lastly we derive the wave-number dependence of fluctuations (the power spectrum) in the two modes, which formed at the above decoupling epoch and are observed in the Friedmann stage. It is found that this can be consistent with the observed spectra of the cosmic microwave background radiation.