AN ANALYTICAL 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 space–time, with a large extra dimension, which is the 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 parametrizations of the same space–time. 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 Ωm = 0.3 today, we find that the cross-over from deceleration to acceleration occurs at z ~ 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 ~ +1.5 to q ~ -0.4 at z ~ 1.17. At the present time q = -0.55 and the equation of state of the universe is w = p/ρ ~ -0.7, in agreement with observations and some theoretical predictions.