On the Possibility of Anisotropic Curvature in Cosmology

TL;DR

This paper explores a class of cosmological models with anisotropic curvature supported by a massless 2-form field, which can produce a preferred direction while maintaining an isotropic CMB at the background level.

Contribution

It introduces a new class of shear-free, anisotropically curved spacetimes with a canonical 2-form field, and tests their observational signatures against CMB and supernova data.

Findings

Supernovae show higher-than-expected dependence on angular position.

Models can produce a preferred direction detectable with future surveys.

Anisotropic curvature can exist without affecting the isotropy of the CMB at the background level.

Abstract

In addition to shear and vorticity a homogeneous background may also exhibit anisotropic curvature. Here a class of spacetimes is shown to exist where the anisotropy is solely of the latter type, and the shear-free condition is supported by a canonical, massless 2-form field. Such spacetimes possess a preferred direction in the sky and at the same time a CMB which is isotropic at the background level. A distortion of the luminosity distances is derived and used to test the model against the CMB and supernovae (using the Union catalog), and it is concluded that the latter exhibit a higher-than-expected dependence on angular position. It is shown that future surveys could detect a possible preferred direction by observing ~ 20 / (\Omega_{k0}^2) supernovae over the whole sky.