We now move on to discuss the second face of the problem of the cosmological constant, which was highlighted recently by the discovery of the acceleration of the universe. This chapter will first review briefly how searching for “dark energy” has come finally to a spatially flat universe well described by a cosmological constant Λ of a size smaller than but nearly comparable to the critical density. For a number of reasons, we consider that this Λ is not a true constant but is mimicked most naturally by a scalar field.

In section 5.1, we sketch what the development has been like mainly on the observational front, culminating in the conclusion that we have an accelerating universe.

As a possible theoretical model discussed recently, we first review in section 5.2 the results of “quintessence,” a name mainly indicating a cosmological scalar field. Since this is a phenomenological approach that is not necessarily constrained rigorously by the scalar–tensor theory, our focus is mainly on the assumed inverse-power potential. A primary concern is the question of how naturally the initial conditions for the scalar field can be chosen. A relevant question is that of whether the scalar-field energy falls off in the same way as the ordinary matter density (“scaling”), or approaches the latter starting from different values (“tracking”).