Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --

Details Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables -- Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --

2006-05-19

arxiv.org/abs/gr-qc/0605108v3

Prog.Theor.Phys.117:17-74,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

58 pages, no figure. Complete version of gr-qc/0605107; some typos are corrected (v2); References and some typos are corrected

Scientific paper

10.1143/PTP.117.17

Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We derive the all components of the Einstein equations in the case where 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 the 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 by the comparison with some literatures.

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