An analytic model for the transition from decelerated to accelerated cosmic expansion

Abstract

We consider the scenario where our observable universe is devised as a dynamical four-dimensional hypersurface embedded in a five-dimensional bulk spacetime, with a large extra dimension, which is the {\it generalization of the flat FRW cosmological metric to five dimensions}. This scenario generates a simple analytical model where different stages of the evolution of the universe are approximated by distinct parameterizations of the {\it same} spacetime. In this model the evolution from decelerated to accelerated expansion can be interpreted as a "first-order" phase transition between two successive stages. The dominant energy condition allows different parts of the universe to evolve, from deceleration to acceleration, at different redshifts within a narrow era. This picture corresponds to the creation of bubbles of new phase, in the middle of the old one, typical of first-order phase transitions. Taking ${\Omega }_m=0.3$ today, we find that the cross-over from deceleration to acceleration occurs at $z\sim 1-1.5$, regardless of the equation of state in the very early universe. In the case of primordial radiation, the model predicts that the deceleration parameter "jumps" from $q\sim +1.5$ to $q\sim -0.4$ at $z\sim 1.17$. At the present time $q=-0.55$ and the equation of state of the universe is $w=p/\rho \sim -0.7$, in agreement with observations and some theoretical predictions.

The abstract and introduction are improved and the discussion section is expanded. A number of references are added

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