  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 between the outer space and 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 it can be consistent with the observed spectra of the cosmic
microwave background radiation.
