Non-linear perturbations in multiple-field inflation

Abstract

We develop a non-linear framework for describing long-wavelength perturbations in multiple-field inflation. The basic variables describing inhomogeneities are defined in a non-perturbative manner, are invariant under changes of time slicing on large scales and include both matter and metric perturbations. They are combinations of spatial gradients generalising the gauge-invariant variables of linear theory. Dynamical equations are derived and supplemented with stochastic source terms which provide the long-wavelength initial conditions determined from short-wavelength modes. Solutions can be readily obtained via numerical simulations or analytic perturbative expansions. The latter are much simpler than the usual second-order perturbation theory. Applications are given in a companion paper.

13 pages, no figures. v4: Included general form of equations of motion and constraints (before fixing gauge); minor textual changes. Matches published version

References in corpus (30)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Non-Gaussianity from Inflation: Theory and Observations
• A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation
• A general proof of the conservation of the curvature perturbation
• Second-Order Cosmological Perturbations from Inflation
• The inflationary prediction for primordial non-gaussianity
• The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
• Primordial non-gaussianities in single field inflation
• Scalar perturbations during multiple-field slow-roll inflation
• Second-order Perturbations of the Friedmann World Model
• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• Evolution of second-order cosmological perturbations
• Large non-Gaussianity in multiple-field inflation
• Non-gaussianity from the second-order cosmological perturbation
• Non-Gaussianity from Preheating
• Evolution of non-linear cosmological perturbations
• Effective noise in stochastic description of inflation
• Non-Gaussian perturbations from multi-field inflation
• Solving the Hamilton-Jacobi Equation for General Relativity
• Non-Gaussian perturbations in hybrid inflation
• Long wavelength iteration of Einstein's equations near a spacetime singularity
• Non-linear inflationary perturbations
• Super-Hubble Nonlinear Perturbations During Inflation
• Simple route to non-Gaussianity in inflation
• On the conservation of second-order cosmological perturbations in a scalar field dominated universe
• Influence of Super-Horizon Scales on Cosmological Observables Generated during Inflation
• Comment about quasi-isotropic solution of Einstein equations near cosmological singularity
• Stochastic approach to inflation II: classicality, coarse-graining and noises
• On second-order superhorizon perturbations in multifield inflationary models
• Coarse-Grained Back Reaction in Single Scalar Field Driven Inflation

Cited by in corpus (86)

• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Primordial Non-Gaussianities from Inflation Models
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• Large non-Gaussianities with Intermediate Shapes from Quasi-Single Field Inflation
• Enhanced Non-Gaussianity from Excited Initial States
• Non-Gaussianity in the modulated reheating scenario
• The shape of primordial non-Gaussianity and the CMB bispectrum
• Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure
• Review of local non-Gaussianity from multi-field inflation
• The inflationary trispectrum
• Large non-Gaussianity in multiple-field inflation
• Non-linear isocurvature perturbations and non-Gaussianities
• One-loop corrections to a scalar field during inflation
• Effective Field Theory and Decoupling in Multi-field Inflation: An Illustrative Case Study
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• Primordial Non-Gaussianity in Multi-Scalar Slow-Roll Inflation
• Quantitative bispectra from multifield inflation
• Stochastic inflation in phase space: Is slow roll a stochastic attractor?
• Nongaussianity from Tachyonic Preheating in Hybrid Inflation
• Two loop stress-energy tensor for inflationary scalar electrodynamics
• Primordial Non-Gaussianities of General Multiple Field Inflation
• Large Nongaussianity from Nonlocal Inflation
• Nonlinear perturbations of cosmological scalar fields
• A Statistical Approach to Multifield Inflation: Many-field Perturbations Beyond Slow Roll
• Lectures on inflation and cosmological perturbations
• One-loop Corrections to Scalar and Tensor Perturbations during Inflation in Stochastic Gravity
• Non-gaussianity of inflationary field perturbations from the field equation
• A parton picture of de Sitter space during slow-roll inflation
• Multifield Cosmological Perturbations at Third Order and the Ekpyrotic Trispectrum
• Moment transport equations for non-Gaussianity
• A Simple Operator Check of the Effective Fermion Mode Function during Inflation
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Non-Gaussian Inflationary Perturbations from the dS/CFT Correspondence
• Predictions for Nongaussianity from Nonlocal Inflation
• Inflationary perturbation theory is geometrical optics in phase space
• Numerical evaluation of the bispectrum in multiple field inflation
• Revisiting non-Gaussianity in multifield inflation with curved field space
• Multifield consequences for D-brane inflation
• The Persistence of Large Scale Structures I: Primordial non-Gaussianity
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Nonlinear perturbations of cosmological scalar fields with non-standard kinetic terms
• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Primordial magnetic fields and nonlinear electrodynamics
• Cosmological UV/IR Divergences and de-Sitter Spacetime
• Primordial non-Gaussianities after Planck 2015: an introductory review
• Stochastic Inflation Revisited: Non-Slow Roll Statistics and DBI Inflation
• Non-Gaussianity from the hybrid potential
• Gauge-invariant quantum gravitational corrections to correlation functions
• Primordial Non-Gaussianities from the Trispectra in Multiple Field Inflationary Models
• Cosmology is not a Renormalization Group Flow
• Perturbative Reheating After Multiple-Field Inflation: The Impact on Primordial Observables
• Wilson Line Inflation
• Multifield inflation beyond $N_{\mathrm{field}}=2$: non-Gaussianities and single-field effective theory
• A geometrical approach to nonlinear perturbations in relativistic cosmology
• Non-Gaussian corrections to the probability distribution of the curvature perturbation from inflation
• Numerical calculation of second order perturbations
• Non-Gaussianities of Single Field Inflation with Non-minimal Coupling
• Hamiltonian formalism for cosmological perturbations: the separate-universe approach
• Cosmological Density Fluctuations in Stochastic Gravity -- Formalism and Linear Analysis --
• Converting entropy to curvature perturbations after a cosmic bounce
• "Finite" Non-Gaussianities and Tensor-Scalar Ratio in Large Volume Swiss-Cheese Compactifications
• Bispectra from two-field inflation using the long-wavelength formalism
• Inflation in Multi-field Modified DBM Potentials
• The Non-Minimal Ekpyrotic Trispectrum
• Predictions in multifield models of inflation
• Generating the primordial curvature perturbations in preheating
• Quantum diffusion and large primordial perturbations from inflation
• Gauge-invariant perturbations at second order in two-field inflation
• Nonlinear superhorizon perturbations of non-canonical scalar field
• Stochastic Samples versus Vacuum Expectation Values in Cosmology
• On primordial trispectrum from exchanging scalar modes in general multiple field inflationary models
• Momentum dependence of the bispectrum in two-field inflation
• Different approaches to the second order Klein-Gordon equation
• Non-Gaussianity in two-field inflation beyond the slow-roll approximation
• The Origin of the Large-Scale Structure in the Universe: Theoretical and Statistical Aspects
• Covariant second-order perturbations in generalized two-field inflation
• Cosmic Acceleration Driven by Mirage Inhomogeneities
• Second-order cosmological perturbations produced by scalar-scalar coupling during inflation stage
• 'Constraint consistency' at all orders in Cosmological perturbation theory
• Bunch-Davies initial conditions and non-perturbative inflationary dynamics in Numerical Relativity
• Primordial Black Holes in non-linear perturbation theory
• Cosmic inflation in non-perturbative quantum gravity
• Non-Gaussianity in D3-brane inflation
• On Inflation and Reheating Features in the Higgs-$R^2$ Model