Nonlinear perturbations of cosmological scalar fields

Abstract

We present a covariant formalism for studying nonlinear perturbations of scalar fields. In particular, we consider the case of two scalar fields and introduce the notion of adiabatic and isocurvature covectors. We obtain differential equations governing the evolution of these two covectors, as well as the evolution equation for the covector associated with the curvature perturbation. The form of these equations is very close to the analogous equations obtained in the linear theory, but our equations are fully nonlinear and exact. As an application of our formalism, we expand these equations at second order in the perturbations. On large scales, we obtain a closed system of coupled scalar equations giving the evolution of the second-order adiabatic and entropy perturbations in terms of the first-order perturbations. These equations in general contain a nonlocal term which, however, rapidly decays in an expanding universe.

45 pages. v3: corrected Eqs. (213), (220), (221) and (225)

References in corpus (7)

• Non-Gaussianities in two-field inflation
• Nongaussian and nonscale-invariant perturbations from tachyonic preheating in hybrid inflation
• Very Large Primordial Non-Gaussianity from multi-field: Application to Massless Preheating
• Gauge-invariant Formulation of the Second-order Cosmological Perturbations
• Nonlinear perturbations for dissipative and interacting relativistic fluids
• Second Order Gauge-Invariant Perturbations during Inflation
• Covariant generalization of cosmological perturbation theory

Cited by in corpus (73)

• Ekpyrotic and Cyclic Cosmology
• Relativistic cosmology and large-scale structure
• Perturbations in generalized multi-field inflation
• Curvature and isocurvature perturbations in two-field inflation
• Non-linear isocurvature perturbations and non-Gaussianities
• Inflation, Cosmic Perturbations and Non-Gaussianities
• The Matter Bounce Curvaton Scenario
• Non-Gaussian Density Fluctuations from Entropically Generated Curvature Perturbations in Ekpyrotic Models
• Influence of heavy modes on perturbations in multiple field inflation
• Nongaussianity from Tachyonic Preheating in Hybrid Inflation
• On Features and Nongaussianity from Inflationary Particle Production
• Intuitive understanding of non-gaussianity in ekpyrotic and cyclic models
• A Statistical Approach to Multifield Inflation: Many-field Perturbations Beyond Slow Roll
• Lectures on inflation and cosmological perturbations
• Ekpyrotic Non-Gaussianity -- A Review
• Non-gaussianity of inflationary field perturbations from the field equation
• Multifield Cosmological Perturbations at Third Order and the Ekpyrotic Trispectrum
• Nonperturbative analysis of the evolution of cosmological perturbations through a nonsingular bounce
• Sachs-Wolfe at second order: the CMB bispectrum on large angular scales
• Moment transport equations for non-Gaussianity
• Multi-field DBI inflation: introducing bulk forms and revisiting the gravitational wave constraints
• de Sitter limit of inflation and nonlinear perturbation theory
• Cosmological Backreaction from Perturbations
• Some Aspects of Tachyon Field Cosmology
• Conserved cosmological perturbation in Galileon models
• Combined local and equilateral non-Gaussianities from multifield DBI inflation
• Revisiting non-Gaussianity in multifield inflation with curved field space
• Inflationary trispectrum from graviton exchange
• Nonlinear perturbations of cosmological scalar fields with non-standard kinetic terms
• Nongaussianity from Particle Production During Inflation
• Non-Gaussianity Generated by the Entropic Mechanism in Bouncing Cosmologies Made Simple
• Primordial Non-Gaussianities from the Trispectra in Multiple Field Inflationary Models
• On reaching the adiabatic limit in multi-field inflation
• Multifield inflation beyond $N_{\mathrm{field}}=2$: non-Gaussianities and single-field effective theory
• Non-Gaussianity of superhorizon curvature perturbations beyond $\delta$ N formalism
• Braneworld non-minimal inflation with induced gravity
• Gauge invariant variables for cosmological perturbation theory using geometrical clocks
• DBI inflation with a non-minimally coupled Gauss-Bonnet term
• Numerical calculation of second order perturbations
• Two-field disformal transformation and mimetic cosmology
• Converting entropy to curvature perturbations after a cosmic bounce
• Constraints on scalar and tensor perturbations in phenomenological and two-field inflation models: Bayesian evidences for primordial isocurvature and tensor modes
• Covariant generalization of cosmological perturbation theory
• On Cross-correlations between Curvature and Isocurvature Perturbations during Inflation
• Vector and tensor contributions to the curvature perturbation at second order
• The Non-Minimal Ekpyrotic Trispectrum
• δN versus covariant perturbative approach to non-Gaussianity outside the horizon in multifield inflation
• Scalar field-perfect fluid correspondence and nonlinear perturbation equations
• Non-Minimal Warm Inflation and Perturbations on the Warped DGP Brane with Modified Induced Gravity
• Delta-N formalism for the evolution of the curvature perturbations in generalized multi-field inflation
• Non-linear Preheating with Scalar Metric Perturbations
• Parametric Resonance of Entropy Perturbations in Massless Preheating
• Nonlinear superhorizon perturbations of non-canonical scalar field
• Tackling non-linearities with the effective field theory of dark energy and modified gravity
• Dynamical evolutin of quintessence dark energy in collapsing dark matter halos
• Coupling structure of multi-field primordial perturbations
• Two-field inflation with non-minimal coupling
• Fully non-linear equivalence of delta N and covariant formalisms
• Covariant Bardeen Perturbation Formalism
• Quantization of perturbations during inflation in the 1+3 covariant formalism
• Non-Gaussianity in Island Cosmology
• A general proof of the equivalence between the δN and covariant formalisms
• Inflation and Scale-invariant $R^2$-Gravity
• Preheating in an Asymptotically Safe Quantum Field Theory
• Comments on gauge-invariance in cosmology
• Gradient expansion of superhorizon perturbations in G-inflation
• $\Delta N$ Formalism and Conserved Currents in Cosmology
• Simulation studies of dark energy clustering induced by the formation of dark matter halos
• 'Constraint consistency' at all orders in Cosmological perturbation theory
• Hamiltonian formalism of cosmological perturbations and higher derivative theories
• Slow-roll corrections in multi-field inflation: a separate universes approach
• Non-linear effects in early Universe cosmology
• Separate universe in multifield inflation: a phase-space approach