Quintessence and the cosmological constant

The idea of quintessence originates from an attempt to understand the smallness of the “cosmological constant” or dark energy in terms of the large age of the universe [1]. As a characteristic consequence, the amount of dark energy may be of the same order of magnitude as radiation or dark matter during a long period of the cosmological history, including the present epoch. Today, the inhomogeneous energy density in the universe – dark and baryonic matter – is about ρinhom ≈ (10eV). This number is tiny in units of the natural scale given by the Planck mass Mp = 1.22 ·10 GeV. Nevertheless, it can be understood easily as a direct consequence of the long duration of the cosmological expansion: a dominant radiation or matter energy density decreases ρ ∼ M p t and the present age of the universe is huge, t0 ≈ 1.5 · 10 yr. It is a natural idea that the homogeneous part of the energy density in the universe – the dark energy – also decays with time and therefore turns out to be small today. A simple realization of this idea, motivated by the anomaly of the dilatation symmetry, considers a scalar field φ with an exponential potential [1]