Description
We extend the gradient-expansion (separate-universe) approach to anisotropic inflationary backgrounds driven by a scalar field coupled to a U(1) gauge field. By choosing an appropriate gauge, we establish a correspondence between linear perturbations and background variations, where the background geometry is given by Bianchi type I spacetimes. We identify a conserved quantity W that generalizes the Wronskian for adiabatic modes. Using this, we show that the comoving curvature perturbation does not freeze on superhorizon scales — it retains memory of the anisotropic phase even after the universe becomes isotropic. Furthermore, we derive a direct relation between the spatial curvature and a gravitational-wave mode, revealing how scalar perturbations can source tensor modes in the presence of anisotropy.