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Prog. Theor. Phys. Vol. 121 No. 6 (2009) pp. 1321-1360
Consistency of Equations in the Second-Order Gauge-Invariant Cosmological Perturbation Theory
Kouji Nakamura
Department of Astronomical Science, The Graduate University
for Advanced Studies, Mitaka 181-8588, Japan
(Received January 4, 2009)
Abstract:
Along the general framework of the gauge-invariant
perturbation theory developed in the papers [K. Nakamura,
Prog. Theor. Phys. 110 (2003), 723; Prog. Theor. Phys.
113 (2005), 481], we rederive the second-order Einstein
equation on four-dimensional homogeneous isotropic background
universe in a gauge-invariant manner without ignoring any mode
of perturbations.
We consider the perturbations both in the universe dominated by
the single perfect fluid and in that dominated by the single scalar field.
We also confirmed the consistency of all the equations of the
second-order Einstein equation and the equations of motion for
matter fields, which are derived in the paper [K. Nakamura, arXiv:0804.3840].
This confirmation implies that all the derived equations of the
second order are self-consistent and these equations are
correct in this sense.
Subject Index :
450, 451
URL :
http://ptp.ipap.jp/link?PTP/121/1321/
DOI : 10.1143/PTP.121.1321
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