Anisotropic separate universe and Weinberg's adiabatic mode

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