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Anisotropic separate universe and Weinberg's adiabatic mode

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arxiv 2101.05707 v1 pith:X4MRIGML submitted 2021-01-14 astro-ph.CO gr-qchep-phhep-th

classification astro-ph.COgr-qchep-phhep-th
keywords universeseparateapproachdeltaformalismadiabaticanisotropicdiffeomorphism
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta{N}$ formalism

    gr-qc 2026-04 unverdicted novelty 8.0 of 10

    A shear-free locally FLRW lattice framework for single-field inflation captures spatially varying expansion, curvature corrections, and nonlinear δN observables at a fraction of the cost of full numerical relativity.

  2. How Dilatation Invariance Suppresses Loop Corrections to Curvature Perturbations on CMB Scales

    astro-ph.CO 2026-08 conditional novelty 5.0 of 10

    Dilatation invariance forces the non-linear curvature perturbation on super-Hubble scales to depend only on the decaying/growing mode, suppressing loop corrections to the CMB power spectrum even with sharp transitions.

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