ar X iv : g r - qc / 0 10 30 93 v 1 2 6 M ar 2 00 1 The shear dynamics in Bianchi I cosmological model on the brane

The shear dynamics in Bianchi I cosmological model on the brane with a perfect fluid (the equation of state is p = (γ −1)µ) is studied. It is shown that for 1 < γ < 2 the shear parameter has maximum at some moment during a transition period from nonstandard to standard cosmology. An exact formula for the matter density µ in the epoch of maximum shear parameter as a function of the equation of state is obtained. In recent several years a lot of effort has been done on the idea that our Universe is a boundary of a space-time manifold with a larger number of dimensions [1]. The cosmological evolution of a three-brane in five dimensional space-time become the matter of intense investigations. The corrections to Ein-stein equations on the brane arising from the influence of a bulk geometry on the brane were obtained [2]. The corresponding cosmological dynamics was studied in detail for a FRW Universe. It was shown that the dynamics of the early brane Universe can differ significantly from the standard scenario [3]. On the other hand, the standard FRW cosmology for the late Universe (when the matter density on the brane µ become negligible in comparison with the brane tension λ) was recovered [4]. Later on this analisys has been done for an anisotropic Bianchi I metric on the brane. The matter source was chosen in the form of a massive scalar field [5] or perfect fluid with the equation of state p = (γ − 1)µ [6]. One of the most interesting results obtained in this way is that the initial singularity, being anisotropic in ordinary cosmology (with the exception of the maximally stiff fluid case [7]), becomes isotropic in the brane cosmology for γ ∈ (1, 2)[5, 6]. Since during the evolution of the brane Universe its dynamics approaches the standard one, later stages of the Universe are isotropic for γ < 2. So, the intermediate stage of a relatively high anisotropy can exist if the matter filling the Universe has a positive pressure. Intuitively we could expect that the 1