The scale factor in a Universe with dark energy

Abstract

The solution of the Friedmann cosmological equations for the scale factor in a model of the Universe containing matter having the equation of state of dust and dark energy is considered. The equation-of-state parameter of the dark energy is taken to be an arbitrary constant w = −1.006 ± 0.045, whose value is constrained by the current observational limits. An exact solution for the scale factor as a function of physical time and conformal time is obtained. Approximate solutions have been found for the entire admissible conformal time interval with an accuracy better than 1%, which exceeds the accuracy of the determined global parameters of our Universe. This is the first time an exact solution for the scale factor describing the evolution of the Universe in a unified way, beginning with the matter-dominated epoch and ending with the infinitely remote future, has been obtained.