Spatial anisotropies from long wavelength scalar and tensor modes

TL;DR

This paper explores how superhorizon scalar and tensor fluctuations influence the geometry of a matter-dominated universe, revealing that long-wavelength modes can induce spatial curvature and shear consistent with certain Bianchi cosmologies.

Contribution

It demonstrates that combined scalar and tensor superhorizon modes can be effectively described by geometries akin to Bianchi types I, V, and IX, extending the conventional separate-universe approach.

Findings

Scalar modes induce spatial curvature.

Tensor modes generate shear.

Effective metrics match Bianchi cosmologies.

Abstract

We investigate the dominant physical effects of superhorizon fluctuations in a flat FLRW 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.