We once again reference Theorem 6.1.2 of the book by Ellis, Maartens, and MacCallum in order to argue that if there is a non zero initial scale factor, that there is a partial breakdown of the Fundamental Singularity theorem which is due to the Raychaudhuri equation. Afterwards, we review a construction of what could happen if we put in what Ellis, Maartens, and MacCallum call the measured effe...

We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary selfinteraction potential in the language of jet bundles and extensions of vector fields. In this framework, the Bianchi— scalar field equations become subsets of the second Bianchi jet bundle, J , and every Bianchi cosmology is naturally extended to live on a variety of J . We are interes...

The global properties of spatially homogeneous cosmological models with collisionless matter are studied. It is shown that as long as the mean curvature of the hypersurfaces of homogeneity remains finite no singularity can occur in finite proper time as measured by observers whose worldlines are orthogonal to these hypersurfaces. Strong cosmic censorship is then proved for the Bianchi I, Bianch...

The scalar field degree of freedom in Einstein’s plus Matter field equations is decoupled for Bianchi type I and V general cosmological models. The source, apart from the minimally coupled scalar field with arbitrary potential V (Φ), is provided by a perfect fluid obeying a general equation of state p = p(ρ). The resulting ODE is, by an appropriate choice of final time gauge affiliated to the s...

We study five dimensional cosmological models with four dimensional hipersufaces of the Bianchi type I and V. In this way the five dimensional vacuum field equations GAB = 0, led us to four dimensional matter equations Gμν = Tμν and the matter is interpreted as a purely geometrical property of a fifth dimension. Also, we find that the energy-momentum tensor induced from the fifth dimension has ...