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The current status of the recent developments of the second-ordergauge-invariant cosmological perturbation theory is reviewed. To show theessence of this perturbation theory, we concentrate only on the universe filledwith a single scalar field. Through this review, we point out the problemswhich should be clarified for the further theoretical sophistication of thisperturbation theory. We also expect that this theoretical sophistication willbe also useful to discuss the theoretical predictions of Non-Gaussianity in CMBand comparison with observations.

Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status