Ponente
Abstract
The Cosmological Principle is applied to a 5D Ricci-flat (bulk) manifold. The general solution is given explicitly in the form of a single metric, namely ‘M-metric’, for every sign of the space curvature, both in the 4+1 and the 3+2 case. Friedmann-Robertson-Walker (FRW) metrics are obtained by projecting the ‘mother’ M-metric onto specific 3+1 (brane) hypersurfaces (top-down approach).
This Kaluza-Klein formalism allows a very intuitive (graphical) approach to the problem of the origin of the Universe. Apart from the standard Big Bang paradigm, one can easily build models for emergent universes (arising from a quasi-stationary state) or even for models with a dynamical signature change, in the philosophy of the Hartle-Hawking ‘no boundary’ approach. A simple toy model is presented, showing a ‘Big unfreeze’ transition from a Riemannian (4D) to a pseudo-Riemannian (3+1) manifold with a radiation-dominated behavior at the beginning of time and a Cosmological-constant asymptotic behavior in the final expansion stage.
