\bf $\delta M$ Formalism: A New Approach to Cosmological Perturbation Theory in Anisotropic Inflation

Abstract

We study the evolution of the metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the $\delta M$ formalism for calculating the evolution of the linear tensor perturbations in anisotropic inflation models in {\it almost} the same way that the so-called $\delta N$ formula is applied to the super-horizon dynamics of the curvature perturbations. Similar to her twin formula, $\delta N$, this new method can substantially reduce the amount of calculations related to the evolution of tensor modes. However, it is not as general as $\delta N$, it is a "perturbative" formula and solves the shear only to linear order. In other words, it is restricted to weak shear limit.

35 pages, 2 figures

References in corpus (20)

• Vector Inflation
• Theory of cosmological perturbations in an anisotropic universe
• Scalar-Scalar, Scalar-Tensor, and Tensor-Tensor Correlators from Anisotropic Inflation
• How isotropic is the Universe?
• Predictions from an anisotropic inflationary era
• Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB
• Multi-brid inflation and non-Gaussianity
• Non-gaussianity from the second-order cosmological perturbation
• Anisotropic Inflation from Vector Impurity
• Primordial Non-Gaussianity in Multi-Scalar Slow-Roll Inflation
• Anisotropic Inflation from Charged Scalar Fields
• Tensor Squeezed Limits and the Higuchi Bound
• Gradient expansion approach to nonlinear superhorizon perturbations
• Non-Gaussian Correlations Outside the Horizon
• Gravity Waves Signatures from Anisotropic pre-Inflation
• Non-Gaussianity of superhorizon curvature perturbations beyond $\delta$ N formalism
• Gradient expansion approach to nonlinear superhorizon perturbations II -- a single scalar field --
• Nonlinear superhorizon perturbations of non-canonical scalar field
• Full nonlinear growing and decaying modes of superhorizon curvature perturbations
• 3+1 Approach to the Long Wavelength Iteration Scheme

Cited by in corpus (13)

• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Stochastic Effects in Anisotropic Inflation
• Single-Field Consistency relation and $\delta N$-Formalism
• Stochastic Effects in Axion Inflation and Primordial Black Holes Formation
• Charged Vector Inflation
• Anisotropic separate universe and Weinberg's adiabatic mode
• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
• On the constant roll complex scalar field inflationary models
• \bf $\delta M$ Formalism and Anisotropic Chaotic Inflation Power Spectrum
• EBWeyl: a Code to Invariantly Characterize Numerical Spacetimes
• Curvature Perturbations in the Effective Field Theory of Inflation
• $\delta N$ formalism on the past light-cone
• Spatial anisotropies from long wavelength scalar and tensor modes