Spatial anisotropies from long wavelength scalar and tensor modes

We investigate the dominant physical effects of superhorizon fluctuations in a flat Friedmann-Lemaitre-Robertson-Walker universe, focusing on whether the combined evolution of scalar and tensor adiabatic modes in the near-horizon regime could lead to geometries beyond those predicted by the conventional separate-universe approach. Assuming a matter-dominated universe and working to first order in perturbations but second order in a gradient expansion, we identify modes that are either pure gauge or unsourced, making them observationally irrelevant. This allows us to derive an effective metric that preserves the spatial symmetries of three well-known Bianchi cosmologies, namely, types I, V, and IX. In this framework, scalar perturbations induce spatial curvature, while the shear arises from long-wavelength tensor perturbations.