Hamiltonian formalism for cosmological perturbations: the separate-universe approach

Abstract

The separate-universe approach provides an effective description of cosmological perturbations at large scales, where the universe can be described by an ensemble of independent, locally homogeneous and isotropic patches. By reducing the phase space to homogeneous and isotropic degrees of freedom, it greatly simplifies the analysis of large-scale fluctuations. It is also a prerequisite for the stochastic-inflation formalism. In this work, we formulate the separate-universe approach in the Hamiltonian formalism, which allows us to analyse the full phase-space structure of the perturbations. Such a phase-space description is indeed required in dynamical regimes which do not benefit from a background attractor, as well as to investigate quantum properties of cosmological perturbations. We find that the separate-universe approach always succeeds in reproducing the same phase-space dynamics for homogeneous and isotropic degrees of freedom as the full cosmological perturbation theory, provided that the wavelength of the modes under consideration are larger than some lower bound that we derive. We also compare the separate-universe approach and cosmological perturbation theory at the level of the gauge-matching procedure, where the agreement is not always guaranteed and requires specific matching prescriptions that we present.

arXiv commentDiscussion around equation (4.12) expanded, few minor changes (main conclusions unchanged)

References in corpus (48)

• The Dynamics of General Relativity
• The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang
• A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation
• A new approach to the evolution of cosmological perturbations on large scales
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Formalising the Slow-Roll Approximation in Inflation
• Cosmological perturbations
• The inflationary prediction for primordial non-gaussianity
• On the Generation of a Scale-Invariant Spectrum of Adiabatic Fluctuations in Cosmological Models with a Contracting Phase
• Bouncing Cosmologies: Progress and Problems
• Duality Invariance of Cosmological Perturbation Spectra
• Stochastic Quantum Gravitational Inflation
• Correlation Functions in Stochastic Inflation
• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• Quantum diffusion during inflation and primordial black holes
• The exponential tail of inflationary fluctuations: consequences for primordial black holes
• Primordial Black Holes from Inflation and Quantum Diffusion
• Conserved cosmological perturbations
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Open EFTs, IR Effects and Late-Time Resummations: Systematic Corrections in Stochastic Inflation
• Infrared Correlations in de Sitter Space: Field Theoretic vs. Stochastic Approach
• Non-linear perturbations in multiple-field inflation
• Quantum diffusion beyond slow-roll: implications for primordial black-hole production
• Ultra-slow-roll inflation with quantum diffusion
• Stochastic Inflation:The Quantum Phase Space Approach
• Stochastic inflation in phase space: Is slow roll a stochastic attractor?
• Stochastic inflation beyond slow roll
• A new algorithm for calculating the curvature perturbations in stochastic inflation
• Observational issues in loop quantum cosmology
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Stochastic Ultra Slow Roll Inflation
• The attractive behaviour of ultra-slow-roll inflation
• General relativistic corrections to $N$-body simulations and the Zel'dovich approximation
• Failure of the stochastic approach to inflation beyond slow-roll
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Canonical transformations and squeezing formalism in cosmology
• Hamiltonian approach to 2nd order gauge invariant cosmological perturbations
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• Comment about quasi-isotropic solution of Einstein equations near cosmological singularity
• Stochastic Inflation Revisited: Non-Slow Roll Statistics and DBI Inflation
• Stochastic inflation at all order in slow-roll parameters: foundations
• Four-mode squeezed states: two-field quantum systems and the symplectic group $\mathrm{Sp}(4,\mathbb{R})$
• Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach
• Stochastic non-attractor inflation
• Hamiltonian theory of classical and quantum gauge invariant perturbations in Bianchi I spacetimes
• Unavoidable shear from quantum fluctuations in contracting cosmologies
• Anisotropic separate universe and Weinberg's adiabatic mode
• Stochastic collapse

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• Primordial black holes from stochastic tunnelling
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• The separate-universe approach and sudden transitions during inflation
• Clustering of primordial black holes from quantum diffusion during inflation
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• Stochastic Inflation in General Relativity
• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
• Stochastic inflation with gradient interactions
• Hamiltonian formalism for cosmological perturbations: fixing the gauge
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• Gauge-invariant perturbations at a quantum gravity bounce
• Gauge-fixing and spacetime reconstruction in the Hamiltonian theory of cosmological perturbations
• Stochastic Inflation in Numerical Relativity
• $\delta N$ formalism on the past light-cone
• The validity of separate-universe approach in transient ultra-slow-roll inflation
• Generalized neutrino isocurvature
• $\delta N$ formalism with gradient interactions
• Dynamically generated tilt of isocurvature fluctuations
• Separate universe in multifield inflation: a phase-space approach