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

We present a simple analytical model where the evolution from decelerated to accelerated cosmic 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. PACS: 04.50.+h; 04.20.Cv