A general proof of the conservation of the curvature perturbation

Abstract

Without invoking a perturbative expansion, we define the cosmological curvature perturbation, and consider its behaviour assuming that the universe is smooth over a sufficiently large comoving scale. The equations are simple, resembling closely the first-order equations, and they lead to results which generalise those already proven in linear perturbation theory and (in part) in second-order perturbation theory. In particular, the curvature perturbation is conserved provided that the pressure is a unique function of the energy density.

9 pages, revtex4, no figures; v2: 14 pages, main body and appendix extended, typos corrected, references added; v3: minor changes, typos corrected, references added

References in corpus (1)

• Non-Gaussian perturbations in hybrid inflation

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• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• Multi-chaotic inflation with and without spectator field
• Suppressed Non-Gaussianity in the Curvaton Model
• Testing gravity with non-Gaussianity
• Stochastic inflation with gradient interactions
• Spectral Index and Non-Gaussianity in Supersymmetric Hybrid Inflation
• Scalar induced gravitational waves review
• Hubble induced mass after inflation in spectator field models
• Gradient expansion of superhorizon perturbations in G-inflation
• Impact of nonlinear overdensity statistics on primordial black hole abundance
• Generation of perturbation after multi-field inflation
• Generically large nongaussianity in small multifield inflation
• Nonminimally Assisted Inflation: A General Analysis
• Axionlike Origin of the Primordial Density Perturbation
• Covariant second-order perturbations in generalized two-field inflation
• Spatial Curvature from Super-Hubble Cosmological Fluctuations
• Constraints on variations in inflaton decay rate from modulated preheating
• Generalized disformal invariance of cosmological perturbations with second-order field derivatives
• Non-perturbative $\delta N$
• Curvaton as dark matter with secondary inflation
• Curvature Perturbation and Domain Wall Formation with Pseudo Scaling Scalar Dynamics
• Towards an Observational Appraisal of String Cosmology
• Loop corrections to primordial fluctuations from inflationary phase transitions
• Inflation with Stochastic Boundary
• Non-Gaussianity in the Cosmic Microwave Background Induced by Dipolar Dark Matter
• $\Delta N$ Formalism and Conserved Currents in Cosmology
• Relics of spatial curvature in the primordial non-gaussianity
• Comoving curvature perturbation in Jordan and Einstein frames
• Affleck-Dine baryogenesis with modulated reheating
• Rolling in the Modulated Reheating Scenario
• Large Scale Cosmic Perturbation from Evaporation of Primordial Black Holes
• Cosmological Perturbations: Vorticity, Isocurvature and Magnetic Fields
• Thermal Effects and Sudden Decay Approximation in the Curvaton Scenario
• A new approach for simulating PBH formation from generic curvature fluctuations with the Misner-Sharp formalism
• The running curvaton
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Cosmic perturbations, baryon asymmetry and dark matter from the minimal supersymmetric standard model
• Affleck-Dine baryogenesis in inflating curvaton scenario with O($10-10^2$TeV) mass moduli curvaton
• The Non-Gaussianity of Racetrack Inflation Models
• Initial conditions of the universe: A sign of the sine mode
• The spatial gauge-dependence of single-field inflationary bispectra
• On non-linear CMB temperature anisotropy from gravitational perturbations
• Implications for Pulsar Timing Arrays of Sub-solar Black Hole Detections: From LVK to Einstein Telescope and Cosmic Explorer
• Non-Gaussianities and Primordial Black Holes
• Entropy Perturbations in N-flation
• Delta-N Formalism for Curvaton with Modulated Decay
• Long-wavelength non-linear perturbations of a complex scalar field
• Lecture notes on non-Gaussianity
• EBWeyl: a Code to Invariantly Characterize Numerical Spacetimes
• On the breakdown of the curvature perturbation ζ during reheating
• Contributions from primordial non-Gaussianity and General Relativity to the galaxy power spectrum
• Dip and non-linearity in the curvature perturbation from inflation with a transient non-slow-roll stage
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• Scale dependences of local form non-Gaussianity parameters from a DBI isocurvature field
• Manifestly gauge invariant theory of the nonlinear cosmological perturbations in the leading order of the gradient expansion
• Curvature perturbation from velocity modulation
• Primordial black holes from the ultraslow-roll phase in the inflaton--curvaton mixed field inflation
• Non-gaussianity and Statistical Anisotropy in Cosmological Inflationary Models
• The R-axion and non-Gaussianity
• Curvature Perturbations in the Effective Field Theory of Inflation
• Escape from the swamp with spectator
• Ultraviolet Sensitivity of Peccei-Quinn Inflation
• Effects of Variable Newton Constant During Inflation
• Relativistic and non-Gaussianity contributions to the one-loop power spectrum
• Improved quantum algorithm for calculating eigenvalues of differential operators and its application to estimating the decay rate of the perturbation distribution tail in stochastic inflation
• Non-linear effects on the Cosmological Gravitational Wave Background anisotropies
• Cosmological Signatures of Neutrino Seesaw Mechanism
• Cosmological Non-Gaussianity from Neutrino Seesaw Mechanism
• Primordial black holes from a curvaton: the role of bimodal distributions
• Spectral index and running of $g_{NL}$ from an isocurvature scalar field
• Uniform Rate Inflation
• Deriving super-horizon curvature perturbations from the dynamics of preheating
• Nonlinear Perturbations in a Variable Speed of Light Cosmology
• Hamiltonian formalism of cosmological perturbations and higher derivative theories
• Primordial non-Gaussianity in noncanonical warm inflation: three- and four-point correlations
• 'Constraint consistency' at all orders in Cosmological perturbation theory
• Evolution of the spectral index after inflation
• Secondary isocurvature perturbations from acoustic reheating
• Mixed perturbations from an Inflaton and Two Curvatons - towards understanding non-gaussianity in more complicated curvaton scenarios
• Thermal Inflation with a Thermal Waterfall Scalar Field Coupled to a Light Spectator Scalar Field
• The quantum origin of cosmic structure: theory and observations
• Curvaton mechanism after multi-field inflation
• $\Delta \mathcal{N}$ and the stochastic conveyor belt of Ultra Slow-Roll
• The Size of Local Bispectrum and Trispectrum in a Non-Minimal Inflation
• $\delta N$ formalism on the past light-cone
• Stochastic Inflation with Interacting Noises
• Observable predictions of generalised inflationary scenarios
• Curvature perturbations from kinetic preheating after $\alpha$-attractor inflation
• Stochastic-tail of the curvature perturbation in hybrid inflation
• Primordial Black Holes in non-linear perturbation theory
• QCD Axions and CMB Anisotropy
• de Sitter symmetries and inflationary scalar-vector models
• Construction of the Conserved Non-linear Zeta via the Effective Action for Perfect Fluids
• Spectator fields and their imprints on the Cosmic Microwave Background
• Higher Order Perturbations Around Backgrounds with One Non-Homogeneous Dimension
• Inflation: a quantum laboratory on cosmological scales
• Remarks on non-gaussian fluctuations of the inflaton and constancy of ζoutside the horizon
• Cosmon as the Modulon: Non-Gaussianity from Dark Energy
• Time-reversed Stochastic Inflation
• Generalized local ansatz for scale-dependent primordial non-Gaussianities and future galaxy surveys
• Curvature perturbations from vacuum transition during inflation
• $\delta N$ formalism with gradient interactions
• Brane structure from a scalar field in general covariant Horava-Lifshitz gravity
• Phase transition catalyzed by primordial black holes
• Conservation of nonlinear curvature perturbations on super-Hubble scales
• Non-linear effects in early Universe cosmology
• On the four-dimensional effective theories in brane-worlds
• Imprints of intrinsic and exterior curvatures in cosmology
• Slow-roll corrections in multi-field inflation: a separate universes approach
• On the coupling of vector fields to the Gauss-Bonnet invariant
• Holographic beta function in de Sitter space
• The Black Hole Window on Cosmic Inflation
• Study of General Relativity and $f(R)$ Modified Gravity with Cosmological Constant for Einstein and Jordan Frames
• Non-Gaussianity in Cosmology: from Inflation to the CMB
• Primordial Black Holes: A Review of Formation and Evolution
• Non-Gaussianity after many-field reheating
• Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta N$ formalism
• Primordial Fluctuations in String Cosmology
• Cosmological long-wavelength solutions in non-adiabatic multi-fluid systems
• Dynamically generated tilt of isocurvature fluctuations
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting
• Separate universe in multifield inflation: a phase-space approach
• Non-Gaussianity in D3-brane inflation
• Ringing Non-Gaussianity from inflation with a step in the second derivative of the potential
• New leading contributions to non-gaussianity in single field inflation
• Construction and applications of the manifestly gauge invariant expressions of the solutions of the cosmological perturbation theory
• Spatial averaging and a non-Gaussianity
• Aspects of inflation and the very early universe
• Uniform rate inflation on the brane
• A Demonstration of Spectral Level Reconstruction of Intrinsic $B$-mode Power
• Inflationary spectral tilts as a result of the dilatation symmetry breaking
• Testing Inflationary Cosmology