Shear-free anisotropic cosmological models

Abstract

A class of orthogonal, spatially homogeneous shear-free cosmological models with an imperfect liquid matter content is considered. It is shown that, for these models, the anisotropic stresses are related to the anisotropic curvature of the spatial hypersurfaces through the electric part of the Weyl tensor. This creates a counterbalance effect which has important consequences for the evolution of the cosmological models. Such features are discussed, and, as an application, some eternally anisotropic models with an imperfect fluid stress tensor which exhibit FRW-like behaviour are given.

On spacetimes admitting shear-free, irrotational, geodesic time-like congruences

“…However, only Bianchi types I, V, VII 0 , V I I h and IX can give rise to FRW models. Indeed, Mimoso and Crawford [14] recently drew attention to the same fact: \No anisotropic model can simultaneously exhibit a perfect uid matter content and a shear-free timelike congruence : : : But the possibility still exists of considering an imperfect uid for shear-free anisotropic models" (where presumably the authors mean a shear-free timelike uid congruence, otherwise the statement i s u n true | see section 6).…”

Constraining anisotropy of the universe from different groups of type-Ia supernovae

“…Using the hemisphere comparison method, Antoniou and Perivolaropoulos [23] found that the highest expansion direction of the universe points towards −0. 28 . Kalus et al [25] tested the anisotropy of the local universe using low-redshift (z < 0.2) SNe Ia data calibrated from four different light curve fitters.…”

“…As regards the theoretical aspect, some anisotropic cosmological models have been studied [28][29][30][31]. We note that the Finsler-Randers spacetime [32][33][34][35] provides an appropriate framework for the anisotropic cosmology.…”

Isotropization of the universe during inflation

“…Indeed, we can imagine models where the expansion is isotropic (i.e., σ ij = 0), but the curvature of the spatial sections is not. These models are known as shear-free cosmologies [51,52].…”

“…Clearly, the condition σ µν = 0 leads to π µν = 2E µν . The remarkable consequence of this choice is that, for the BIII and KS metrics, the background equations are formally the Friedmann equations with spatial curvature [51,56]. Thus, at the background level, slow-roll inflation will proceed exactly as in a FL universe, and the spatial anisotropy will be diluted as 1/S 2 , as usual.…”