The role of dark energy in the evolution of the universe

Abstract

We consider the solution of the Einstein equations for a universe with a positive cosmological constant (or equivalently possessing a finite uniform vacuum/dark energy density) within a conformal metric, rather than the usual Robertson-Walker metric. In terms of the associated coordinates the expansion and evolution of the resulting universe is vastly different from the standard de Sitter solution. The conformal metric enables one to impose the conservation of the total energy of the universe through a suitable choice of the scale factor. This global function is no longer part of the metric or controlled by the Einstein equations, but rather is fixed by energy conservation. The solution describes a linearly - rather than the usual exponentially - expanding universe. In lowest order this expansion remains linear in the presence of matter and radiation, so that the proportions of dark energy and matter are not fixed strongly by the supernovae data and must be deduced from other astronomical data. One of the big mysteries of the standard model, namely that the density is such that the universe balances exactly between the expanding and contracting mode, is resolved naturally. The homogeneity and isotropy can be explained without introducing more exotic explanations such as inflation. The simplest model with only dark energy present already gives a good description of the supernovae data, while the current acceleration suggested by these data could well be due to the conversion of matter into radiation. The model implies an age of the universe of 13.8 billion years, which is in good agreement with the recent consensus. Consequences of the dual representations of the universe (either in terms of the original variables or in terms of co-moving coordinates) are reviewed. One of these consequence is that the age of the universe, as measured by a co-moving observer, remains constant over time.