Gauge-invariant Formulation of the Second-order Cosmological Perturbations

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 non-linear effects of the Einstein equations.

arXiv comment5 pages, no figure. RevTeX; short letter version of gr-qc/0605108; some details of explanations are added

References in corpus (29)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Non-Gaussianity from Inflation: Theory and Observations
• A general proof of the conservation of the curvature perturbation
• Second-Order Cosmological Perturbations from Inflation
• Relativistic second-order perturbations of the Einstein-de Sitter Universe
• Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
• On Non-Gaussianity in the Curvaton Scenario
• Second-order Perturbations of the Friedmann World Model
• Evolution of second-order cosmological perturbations
• Non-gaussianity from the second-order cosmological perturbation
• Conserved non-linear quantities in cosmology
• Evolution of non-linear cosmological perturbations
• Magnetic field generation from cosmological perturbations
• Gauge-Invariant Temperature Anisotropies and Primordial Non-Gaussianity
• Large-scale magnetic fields from density perturbations
• Evolution of Second-Order Cosmological Perturbations and Non-Gaussianity
• The Full Second-Order Radiation Transfer Function for Large-Scale CMB Anisotropies
• Relativistic second-order perturbations of nonzero-Λflat cosmological models and CMB anisotropies
• Gauge Invariant Variables in Two-Parameter Nonlinear Perturbations
• Enhancement of Non-Gaussianity after Inflation
• Gauge dependence in the theory of non-linear spacetime perturbations
• On the conservation of second-order cosmological perturbations in a scalar field dominated universe
• Observables and gauge invariance in the theory of non-linear spacetime perturbations
• Second Order Gauge Invariant Perturbation Theory -- Perturbative curvatures in the two-parameter case --
• Second-order gravitational effects of local inhomogeneities on CMB anisotropies and non-Gaussian signatures
• Non-Linear N-Parameter Spacetime Perturbations: Gauge Transformations
• Two-parameter non-linear spacetime perturbations: gauge transformations and gauge invariance
• Second-order gravitational effects of local inhomogeneities on CMB anisotropies in nonzero-Lambda flat cosmological models

Cited by in corpus (48)

• The cosmological gravitational wave background from primordial density perturbations
• Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --
• Gravitational waves from an early matter era
• Constraints on primordial density perturbations from induced gravitational waves
• Nonlinear perturbations of cosmological scalar fields
• Hamiltonian approach to 2nd order gauge invariant cosmological perturbations
• Gravitational waves generated by second order effects during inflation
• Vector modes generated by primordial density fluctuations
• Gauge-invariant quantum gravitational corrections to correlation functions
• Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status
• Primordial magnetic fields from second-order cosmological perturbations: Tight coupling approximation
• Cosmological matching conditions for gravitational waves at second order
• Gauge transformation of scalar induced tensor perturbation during matter domination
• General cosmological perturbations in teleparallel gravity
• Perturbations of Matter Fields in the Second-order Gauge-invariant Cosmological Perturbation Theory
• Note on gauge invariance of second order cosmological perturbations
• Covariant generalization of cosmological perturbation theory
• Analytic solutions of scalar perturbations induced by scalar perturbations
• Ghost and Laplacian Instabilities in the Teleparallel Horndeski Gravity
• Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge
• Construction of gauge-invariant variables of linear metric perturbations on an arbitrary background spacetime
• On the Gauge Invariance of Scalar Induced Gravitational Waves: Gauge Fixings Considered
• A clarification on prevailing misconceptions in unimodular gravity
• Second-order cosmological perturbations. IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stage
• A precise numerical estimation of the magnetic field generated around recombination
• Second-order cosmological perturbations. II. Produced by scalar-tensor and tensor-tensor couplings
• Long wavelength limit of evolution of nonlinear cosmological perturbations
• Second order density perturbations for dust cosmologies
• Perturbation theory for cosmologies with non-linear structure
• On the gauge dependence of scalar induced secondary gravitational waves during radiation and matter domination eras
• Gauge-invariant approach to the parametrized post-Newtonian formalism
• Cosmological Perturbation Theory Revisited
• Comparing different formulations of non-linear cosmological perturbation theory
• General formulation of general-relativistic higher-order gauge-invariant perturbation theory
• The Method of Self-Consistent Field and Macroscopical Einstein Equations for the Early Universe
• Second-order cosmological perturbations. III. Produced by scalar-scalar coupling during radiation-dominated stage
• Relativistic Euler Equations in cosmologies with non-linear structures
• Gauge-invariant variables in general-relativistic perturbations: globalization and zero-mode problem
• Recursive structure in the definitions of gauge-invariant variables for any order perturbations
• A confirmation of agreement of different approaches for scalar gauge-invariant metric perturbations during inflation
• Gauge-invariant post-Newtonian perturbations in symmetric teleparallel gravity
• Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status updated in 2019
• A simplified structure for the second order cosmological perturbation equations
• Second-order cosmological perturbations produced by scalar-scalar coupling during inflation stage
• Manifestly gauge invariant theory of the nonlinear cosmological perturbations in the leading order of the gradient expansion
• Higher Order Perturbations Around Backgrounds with One Non-Homogeneous Dimension
• Second Order perturbation Theory: A covariant approach involving a barotropic equation of state
• Construction and applications of the manifestly gauge invariant expressions of the solutions of the cosmological perturbation theory