Anisotropic separate universe and Weinberg's adiabatic mode

Abstract

In the separate universe approach, an inhomogeneous universe is rephrased as a set of glued numerous homogeneous local patches. This is the essence of the gradient expansion and the $\delta N$ formalism, which have been widely used in solving a long wavelength evolution of the universe. In this paper, we show that the separate universe approach can be generically used, as long as a theory under consideration is local and preserves the spatial diffeomorphism invariance. Focusing on these two conditions, we also clarify the condition for the existence of the so-called Weinberg's adiabatic mode. Remarkably, the separate universe approach and the $\delta N$ formalism turn out to be applicable also to models with shear on large scales and also to modified theories of gravity, accepting violation of four-dimensional diffeomorphism invariance. The generalized $\delta N$ formalism enables us to calculate all the large scale fluctuations, including gravitational waves. We also argue several implications on anisotropic inflation and ultra slow-roll inflation.

48 pages, 1 figure

References in corpus (35)

• Quantum Gravity at a Lifshitz Point
• Resummation of Massive Gravity
• The Effective Field Theory of Inflation
• Healthy theories beyond Horndeski
• Inflationary Universe with Anisotropic Hair
• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• Generation of Large-Scale Magnetic Fields in Single-Field Inflation
• Magnetic fields from inflation?
• Non-Gaussianity as a Particle Detector
• Theory of cosmological perturbations in an anisotropic universe
• On the one loop corrections to inflation and the CMB anisotropies
• The Nature of Primordial Fluctuations from Anisotropic Inflation
• Semiclassical relations and IR effects in de Sitter and slow-roll space-times
• Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB
• Anisotropic Power-law Inflation
• On the One Loop Corrections to Inflation II: The Consistency Relation
• Building a Boostless Bootstrap for the Bispectrum
• Ultra-slow-roll inflation with quantum diffusion
• On the Inflationary Perturbations of Massive Higher-Spin Fields
• IR divergence does not affect the gauge-invariant curvature perturbation
• Anisotropic non-Gaussianity from vector field perturbations
• Soft de Sitter Effective Theory
• Multitracing Anisotropic Non-Gaussianity with Galaxy Shapes
• Inflationary Infrared Divergences: Geometry of the Reheating Surface vs. delta N Formalism
• Detecting higher spin fields through statistical anisotropy in the CMB and galaxy power spectra
• Galaxy imaging surveys as spin-sensitive detector for cosmological colliders
• Gradient expansion approach to nonlinear superhorizon perturbations
• Gravity Waves Signatures from Anisotropic pre-Inflation
• Non-Gaussian Correlations Outside the Horizon
• Non-Gaussianity of superhorizon curvature perturbations beyond $\delta$ N formalism
• Resilience of long modes in cosmological observables
• Solid Consistency
• Solid Soft Theorems
• Large gauge transformation, Soft theorem, and Infrared divergence in inflationary spacetime
• Unavoidable shear from quantum fluctuations in contracting cosmologies

Cited by in corpus (11)

• Review on stochastic approach to inflation
• Stochastic inflation at all order in slow-roll parameters: foundations
• Hamiltonian formalism for cosmological perturbations: the separate-universe approach
• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
• Hamiltonian formalism for cosmological perturbations: fixing the gauge
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• $\delta N$ formalism on the past light-cone
• The validity of separate-universe approach in transient ultra-slow-roll inflation
• Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta N$ formalism
• Separate universe in multifield inflation: a phase-space approach
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function