Gauge-invariant formulation of second-order cosmological perturbations

2006/05/31 by K. Nakamura, Kouji Nakamura · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Solar and Space Plasma Dynamics #astro-ph #gr-qc #hep-ph #hep-th #math-ph #math.MP

paper · pdf · doi:10.1103/physrevd.74.101301

published as Phys.Rev. D74 (2006) 101301 · 5 pages, no figure. RevTeX; short letter version of gr-qc/0605108; some details of explanations are added

arxiv created 2006/09/15 · openalex publication_date 2006/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Gauge-invariant treatments of the second-order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. These equations imply that the tensor and the vector mode of the second-order metric perturbations may be generated by the scalar-scalar mode coupling of the linear order perturbations as the result of the nonlinear effects of the Einstein equations.

Citations

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Non-Gaussianity from Inflation: Theory and Observations
• First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Preliminary Maps and Basic Results
• Non-Gaussianity from the second-order cosmological perturbation

Cited by

• Gauge-invariant quantum gravitational corrections to correlation functions
• Vector modes generated by primordial density fluctuations
• A simplified structure for the second order cosmological perturbation equations
• Gauge-invariant approach to the parametrized post-Newtonian formalism