Prog. Theor. Phys. Vol. 117 No. 1 (2007) pp. 17-74

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Second-Order Gauge Invariant Cosmological Perturbation Theory

— Einstein Equations in Terms of Gauge Invariant Variables —

Kouji Nakamura

Department of Astronomical Science, the Graduate University
for Advanced Studies, Mitaka 181-8588, Japan

(Received May 22, 2006)

Abstract:

Following the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid. 113 (2005), 481], we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive all the components of the Einstein equations in the case that the first-order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that second-order vector and tensor modes may be generated due to the mode-mode coupling of the linear-order scalar perturbations. We also briefly discuss the main progress of this work through comparison with previous works.

URL : http://ptp.ipap.jp/link?PTP/117/17/
DOI : 10.1143/PTP.117.17

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