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arXiv · 2101.05707

Anisotropic separate universe and Weinberg's adiabatic mode

Takahiro Tanaka·Yuko Urakawa
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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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Takahiro Tanaka, Yuko Urakawa. 2021-01-14. Anisotropic separate universe and Weinberg's adiabatic mode. https://doi.org/10.1088/1475-7516/2021/07/051

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