Abstract
A cosmic no-hair theorem for all initially contracting, spatially homogeneous, orthogonal Bianchi Cosmologies is derived - which shows that all such Universes asymptote to a spatially flat, isotropic Universe with the inclusion of a shear viscous stress. This establishes a new mechanism of isotropisation in a contracting Universe, which does not take recourse to an ekpyrosis-like mechanism using an effective ultra-stiff equation of state fluid, that is, one in which the pressure is much greater than the energy density.
Highlights
An additional problem that plagues contracting universe scenarios, such as one that must be incorporated in a bouncing cosmology, is the problem of growing anisotropies and inhomogeneities
We are drawing on previous work on nohair theorems in contracting universes [29] to derive a new no-hair theorem which shows that isotropisation with the aid of shear viscous anisotropic stress is possible in the most general spatially homogeneous Universe
In [16], we have shown that the inclusion of shear viscous stresses leads to isotropisation of a Bianchi Type IX Universe
Summary
In this work, interested in studying the stability of the isotropic Friedmann Lemaitre point. We use the orthonormal frame approach and we can write out the Einstein Field Equations in all generality for the Bianchi Classes A and B. The fluid velocity which is the unit timelike vector is given by ua. The other unknown quantity in (2.10) is the local angular velocity of the spatial frame specified by a set of 1-forms {eα} with respect to a Fermi-propagated spatial frame We shall call this the Fermi rotation which is given by, Ωa. We can choose a frame where nαβ are diagonalised and the Aa can be expressed as (A, 0, 0) via the Jacobi equation. We can show that the shear tensor can be diagonalised in this frame as long as παβ = 0 or παβ ∝ σαβ. Before we begin our analysis of the stability of the isotropic Friedmann-Lemaitre point, we shall review the inclusion of dissipative effects in a cosmology
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