{\delta}M Formalism

We study the evolution of the "non-perturbative" 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 tensor perturbations in anisotropic inflation models in almost similar way as the so-called {\delta}N formula for the super-horizon dynamics of the curvature perturbations. Likewise its ancestor, {\delta}N formalism, this new method can substantially reduce the amount of calculations related to the evolution of the tensor modes.