Evolution of non-linear cosmological perturbations

Abstract

We define fully non-perturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our non-linear generalizations are defined geometrically, independently of any coordinate system. We give the equations governing their evolution on all scales. Also, in order to make contact with previous works on first and second order perturbations, we introduce a coordinate system and show that previous results can be recovered, on large scales, in a remarkably simple way, after restricting our definitions to first and second orders in a perturbative expansion.

4 pages, version published in PRL 95, 091303 (2005)

References in corpus (3)

• Non-Gaussianity from Inflation: Theory and Observations
• A general proof of the conservation of the curvature perturbation
• On the conservation of second-order cosmological perturbations in a scalar field dominated universe

Cited by in corpus (109)

• The inflationary prediction for primordial non-gaussianity
• Towards a Nonsingular Bouncing Cosmology
• Non-Gaussianities in two-field inflation
• Primordial perturbations and non-Gaussianities in DBI and general multi-field inflation
• Perturbations in generalized multi-field inflation
• Primordial trispectrum from inflation
• Curvature and isocurvature perturbations in two-field inflation
• The universe seen at different scales
• Anomaly freedom in perturbative loop quantum gravity
• Non-linear isocurvature perturbations and non-Gaussianities
• Multiple field inflation
• Conserved non-linear quantities in cosmology
• Local non-Gaussianity from inflation
• Non-linear perturbations in multiple-field inflation
• Primordial Non-Gaussianity in Multi-Scalar Slow-Roll Inflation
• Evolution of fNL to the adiabatic limit
• Nonlinear perturbations of cosmological scalar fields
• Non-gaussianity and cosmic uncertainty in curvaton-type models
• Manifestly Gauge-Invariant General Relativistic Perturbation Theory: I. Foundations
• The radiative transfer at second order: a full treatment of the Boltzmann equation with polarization
• Very Large Primordial Non-Gaussianity from multi-field: Application to Massless Preheating
• Lectures on inflation and cosmological perturbations
• Non-Gaussian perturbations from multi-field inflation
• The Zeta-Zeta Correlator Is Time Dependent
• Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation
• Gauge invariant averages for the cosmological backreaction
• Cosmological Perturbations in Unimodular Gravity
• Multifield Cosmological Perturbations at Third Order and the Ekpyrotic Trispectrum
• A note on the equivalence of a barotropic perfect fluid with a K-essence scalar field
• Moment transport equations for non-Gaussianity
• Gauge-invariant Formulation of the Second-order Cosmological Perturbations
• Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order
• Disformal transformation of cosmological perturbations
• Cosmological Backreaction from Perturbations
• Conserved cosmological perturbation in Galileon models
• Hamiltonian approach to 2nd order gauge invariant cosmological perturbations
• Gravitational waves generated by second order effects during inflation
• Nonlinear perturbations of cosmological scalar fields with non-standard kinetic terms
• Primordial perturbations and non-Gaussianities from modulated trapping
• Primordial non-Gaussianities after Planck 2015: an introductory review
• Cancellation of quantum corrections on the soft curvature perturbations
• Review on stochastic approach to inflation
• Stochastic inflation at all order in slow-roll parameters: foundations
• Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multi-component, curvature, and rotation
• Primordial Non-Gaussianities from the Trispectra in Multiple Field Inflationary Models
• A not so short note on the Klein-Gordon equation at second order
• Probability of primordial black hole formation and its dependence on the radial profile of initial configurations
• On reaching the adiabatic limit in multi-field inflation
• Back-Reaction of Super-Hubble Cosmological Perturbations Beyond Perturbation Theory
• Reheating, Multifield Inflation and the Fate of the Primordial Observables
• Inflationary scalar spectrum in loop quantum cosmology
• General treatment of isocurvature perturbations and non-Gaussianities
• Non-Gaussian corrections to the probability distribution of the curvature perturbation from inflation
• A geometrical approach to nonlinear perturbations in relativistic cosmology
• Gauge invariant variables for cosmological perturbation theory using geometrical clocks
• Frame independent cosmological perturbations
• Nonlinear perturbations for dissipative and interacting relativistic fluids
• Preheating and Entropy Perturbations in Axion Monodromy Inflation
• Second order Boltzmann equation : gauge dependence and gauge invariance
• Second Order Gauge-Invariant Perturbations during Inflation
• A relativistic signature in large-scale structure
• Density Perturbations from Modulated Decay of the Curvaton
• Large trispectrum in two-field slow-roll inflation
• Non-Spherical Szekeres models in the language of Cosmological Perturbations
• Covariant generalization of cosmological perturbation theory
• Stochastic Inflation in General Relativity
• On Cross-correlations between Curvature and Isocurvature Perturbations during Inflation
• The Non-Minimal Ekpyrotic Trispectrum
• Primordial Trispectrum from Isocurvature Fluctuations
• Degeneracy between CCDM and $\Lambda$CDM cosmologies
• Non-linear Preheating with Scalar Metric Perturbations
• Nonlinear superhorizon perturbations of non-canonical scalar field
• Cosmological perturbations from multi-field inflation
• Intrinsic Entropy Perturbations from the Dark Sector
• Comparing different formulations of non-linear cosmological perturbation theory
• An update on adiabatic modes in cosmology and $\delta$N formalism
• Holographic Curvature Perturbations in a Cosmology with a Space-Like Singularity
• Coupling structure of multi-field primordial perturbations
• Quantization of perturbations during inflation in the 1+3 covariant formalism
• The Method of Self-Consistent Field and Macroscopical Einstein Equations for the Early Universe
• Covariant Bardeen Perturbation Formalism
• Two-field inflation with non-minimal coupling
• Fully non-linear equivalence of delta N and covariant formalisms
• A general proof of the equivalence between the δN and covariant formalisms
• The Origin of the Large-Scale Structure in the Universe: Theoretical and Statistical Aspects
• Curvaton as dark matter with secondary inflation
• Spatial Curvature from Super-Hubble Cosmological Fluctuations
• A response to criticisms on "CMB Constraints Cast a Shadow on CSL Model"
• Thermal Effects and Sudden Decay Approximation in the Curvaton Scenario
• Long-wavelength non-linear perturbations of a complex scalar field
• Conformal invariant cosmological perturbations via the covariant approach
• On non-linear CMB temperature anisotropy from gravitational perturbations
• Quantitative classicality in cosmological interactions during inflation
• Hamiltonian formalism of cosmological perturbations and higher derivative theories
• 'Constraint consistency' at all orders in Cosmological perturbation theory
• Bunch-Davies initial conditions and non-perturbative inflationary dynamics in Numerical Relativity
• Growth of covariant perturbations in the contracting phase of a bouncing universe
• Covariant perturbations through a simple non-singular bounce
• Construction of the Conserved Non-linear Zeta via the Effective Action for Perfect Fluids
• Observable predictions of generalised inflationary scenarios
• Gravity of Cosmological Perturbations in the CMB
• Remarks on non-gaussian fluctuations of the inflaton and constancy of ζoutside the horizon
• Cosmological Singularities in Brane Gravity
• Higher Order Perturbations Around Backgrounds with One Non-Homogeneous Dimension
• Conservation of nonlinear curvature perturbations on super-Hubble scales
• Cosmological perturbations on an averaged background
• Separate universe in multifield inflation: a phase-space approach
• Conformal invariant cosmological perturbations via the covariant approach: multicomponent universe
• Second Order perturbation Theory: A covariant approach involving a barotropic equation of state