A geometrical approach to nonlinear perturbations in relativistic cosmology

Abstract

We give a pedagogical review of a covariant and fully non-perturbative approach to study nonlinear perturbations in cosmology. In the first part, devoted to cosmological fluids, we define a nonlinear extension of the uniform-density curvature perturbation and derive its evolution equation. In the second part, we focus our attention on multiple scalar fields and present a nonlinear description in terms of adiabatic and entropy perturbations. In both cases, we show how the formalism presented here enables one to easily obtain equations up to second, third and higher orders.

16 pages; invited review article for Classical and Quantum Gravity issue on non-linear cosmology

References in corpus (22)

• Primordial perturbations and non-Gaussianities in DBI and general multi-field inflation
• Primordial trispectrum from inflation
• Primordial fluctuations and non-Gaussianities in multi-field DBI inflation
• Bound-State Effects on Light-Element Abundances in Gravitino Dark Matter Scenarios
• Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion
• Non-gaussianity from the second-order cosmological perturbation
• Local non-Gaussianity from inflation
• Non-Gaussianities from ekpyrotic collapse with multiple fields
• Nongaussianity from Tachyonic Preheating in Hybrid Inflation
• Primordial Non-Gaussianities of General Multiple Field Inflation
• Lectures on inflation and cosmological perturbations
• Non-Gaussianity of quantum fields during inflation
• Multifield Cosmological Perturbations at Third Order and the Ekpyrotic Trispectrum
• Search for 14.4 keV solar axions emitted in the M1-transition of 57Fe nuclei with CAST
• Primordial Trispectrum from Entropy Perturbations in Multifield DBI Model
• Primordial Non-Gaussianity in Models with Dark Matter Isocurvature Fluctuations
• Mixed Bino-Wino-Higgsino Dark Matter in Gauge Messenger Models
• Covariant generalization of cosmological perturbation theory
• Inflation, quantum fluctuations and cosmological perturbations
• On Quantum Effects in Soft Leptogenesis
• Quantization of perturbations during inflation in the 1+3 covariant formalism
• Gravity and non-gravity mediated couplings in multiple-field inflation

Cited by in corpus (29)

• Local non-Gaussianity from inflation
• Evolution of fNL to the adiabatic limit
• Multi-field inflation and cosmological perturbations
• Conserved cosmological perturbation in Galileon models
• Cosmological perturbation theory and quantum gravity
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
• General treatment of isocurvature perturbations and non-Gaussianities
• Second order solutions of cosmological perturbation in the matter dominated era
• Gauge invariance and non-Gaussianity in Inflation
• Large trispectrum in two-field slow-roll inflation
• Density Perturbations from Modulated Decay of the Curvaton
• Primordial Trispectrum from Isocurvature Fluctuations
• General CMB bispectrum analysis using wavelets and separable modes
• δN versus covariant perturbative approach to non-Gaussianity outside the horizon in multifield inflation
• Parametric Resonance of Entropy Perturbations in Massless Preheating
• A balance for Dark Matter bound states
• Quadratic Isocurvature Cross-Correlation, Ward Identity, and Dark Matter
• The interacting vacuum and tensions: a comparison of theoretical models
• On post-inflation validity of perturbation theory in Horndeski scalar-tensor models
• Fully non-linear equivalence of delta N and covariant formalisms
• A general proof of the equivalence between the δN and covariant formalisms
• $\Delta N$ Formalism and Conserved Currents in Cosmology
• Thermal Effects and Sudden Decay Approximation in the Curvaton Scenario
• Structure formation and quasi-spherical collapse from initial curvature perturbations with numerical relativity simulations
• On non-linear CMB temperature anisotropy from gravitational perturbations
• Growth of covariant perturbations in the contracting phase of a bouncing universe
• Covariant perturbations through a simple non-singular bounce
• Observable predictions of generalised inflationary scenarios
• Separate universe in multifield inflation: a phase-space approach