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Anisotropic separate universe : Long-wavelength perturbations and conserved quantities
We investigate the long wavelength evolution of linear perturbations in a homogeneous and anisotropic background with a scalar field coupled to a vector field. Using the spatial gradient expansion in the uniform $\mathcal{N}$ gauge in which the number of $e$ folds is unperturbed, we derive the complete set of superhorizon solutions and establish their correspondence with infinitesimal variations of the homogeneous...