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Advances in Astronomy
Volume 2010, Article ID 576273, 26 pages
Review Article

Second-Order Gauge-Invariant Cosmological Perturbation Theory: Current Status

Optical and Infrared Astronomy Division, National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588, Japan

Received 19 April 2010; Accepted 12 July 2010

Academic Editor: Eiichiro Komatsu

Copyright © 2010 Kouji Nakamura. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The current status of the recent developments of the second-order gauge-invariant cosmological perturbation theory is reviewed. To show the essence of this perturbation theory, we concentrate only on the universe filled with a single scalar field. Through this paper, we point out the problems which should be clarified for the further theoretical sophistication of this perturbation theory. We also expect that this theoretical sophistication will be also useful to discuss the theoretical predictions of non-Gaussianity in CMB and comparison with observations.