Anisotropic separate universe and Weinberg's adiabatic mode

Understand

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.