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A new field theory formulation is presented for the analysis of the CMB powerspectrum distribution in the cosmology. The background-field formalism is fullyused. Stimulated by the recent idea of the {\it emergent} gravity, thegravitational (metric) field $g_\mn$ is not taken as the quantum-field, but asthe background field. The statistical fluctuation effect of the metric field istaken into account by the path (hyper-surface)-integral over the space-time.Using a simple scalar model on the curved (dS$_4$) space-time, we explain theabove things with the following additional points: 1) Clear separate treatmentof the classical effect, the statistical effect and the quantum effect; 2) Thecosmological fluctuation comes not from the 'quantum' gravity but from theunkown 'microscopic' movement; 3) IR parameter ($\ell$) is introduced for thetime axis as the periodicity. Time reversal(Z$_2$)-symmetry is introduced inorder to treat the problem separately with respect to the Z$_2$ parity. Thisprocedure much helps both UV and IR regularization to work well.

New Approach to Cosmological Fluctuation using the Background Field Method and CMB Power Spectrum