Possibility of anisotropic curvature in cosmology

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 $\sim 20/(\Omega _{k0}{}^2)$ supernovae over the whole sky.

Figure 1

Top: 1, 2, and $3\sigma$ confidence-level contours obtained from the SN Ia data. Solid contours stand for the model considered here, thick dashed lines for $\Lambda \mathrm{CDM}$ (marginalized over $H_0$, $u_P$, and $v_P$). Bottom: constraints on the preferred direction in galactic coordinates. Red (darker) and orange (medium) stand for 1 and 2$\sigma$, whereas the light orange (lighter) stand for all regions excluded at more than $2\sigma$ (marginalized over $H_0$, ${\Omega }_{m0}$, and ${\Omega }_{k0}$). Some positions in the sky are marked in the figure as reference.

Figure 2

Constraints on the preferred direction in galactic coordinates for 3 supernova mock catalogs, assuming a LRS metric with ${\Omega }_{k0}=-0.1$ and preferred direction along the vertical axis as the fiducial model. Top: 1000 SNe; middle: 3000 SNe; bottom: 10 000 SNe. Red (darker), orange (medium), and light orange (lighter—bottom plot only) stand for 1, 2, and $3\sigma$, respectively, (marginalized over $H_0$, ${\Omega }_{m0}$, and ${\Omega }_{k0}$). The light orange (lightest) represents the regions excluded at more than $2\sigma$ (above 2 plots) or $3\sigma$ (bottom).