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

TL;DR

This paper presents an analytical five-dimensional cosmological model where the universe transitions from decelerated to accelerated expansion as a first-order phase transition, aligning with observational data.

Contribution

It introduces a novel five-dimensional hypersurface model that describes the universe's transition as a phase change, providing new insights into cosmic acceleration.

Findings

Transition from deceleration to acceleration at redshift z ~ 1-1.5

Deceleration parameter jumps from +1.5 to -0.4 at z ~ 1.17

Current deceleration parameter q = -0.55, equation of state w ~ -0.7

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.