Isotropic Evolution of a JBD Anisotropic Bianchi Universe

Abstract

I study the dynamical effects due to the Brans-Dicke scalar φ-field at the early stages of a supposedly anisotropic Universe expansion in the scalar-tensor cosmology of Jordan-Brans-Dicke. This is done considering the behaviour of the general solutions for the homogeneous model of Bianchi type VII in the vacuum case. I conclude that the Bianchi-VII₀ model shows an isotropic expansion and that its only physical solution is equivalent to a Friedman-Robertson-Walker spacetime whose evolution can, depending on the value of the JBD coupling constant, begin in a singularity and, after expanding (inflating, if ω > 0), shrink to another, or starting in a non-singular state, collapse to a singularity. I also conclude that the general Bianchi-VII _h (with h ≠ 0) models show strong curvature singularities producing a complete collapse of the homogeneity surfaces to 2D-manifolds, to 1D-manifolds or to single points. Our analysis depends crucially on the introduction of the so-called intrinsic time, Φ, as the product of the JBD scalar field φ times a mean scale factor a ³ = a ₁ a ₂ a ₃, in which the finite-cosmological-time evolution of this universe unfolds into an infinite Φ-range. These universes isotropize from an anisotropic initial state, thence I conclude that they are stable against anisotropic perturbations.