2008/12/31 by K. Nakamura, Kouji Nakamura · 12 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmological perturbation theory #Cosmology #Cosmology and Gravitation Theories #Einstein #Einstein equations #Einstein field equations #Equations of motion #Friedmann–Lemaître–Robertson–Walker metric #Galaxies: Formation, Evolution, Phenomena #Gauge theory #General relativity #Invariant (physics) #Isotropy #Mathematical physics #Perfect fluid #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum mechanics #Scalar field #Theoretical physics #Universe #astro-ph #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1143/ptp.121.1321
published in Progress of Theoretical Physics 121(6), 1321-1360 (Oxford University Press) · (v1) 38pages, no figure; (v2) Typos and references are corrected
arxiv created 2009/01/03 · openalex publication_date 2009/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.