Cosmological tracking solutions - art. no. 123504

A substantial fraction of the energy density of the universe may consist of quintessence in the form of a slowly rolling scalar field. Since the energ y density of the scalar field generally decreases more slowly than the matt er energy density, it appears that the ratio of the two densities must be s et to a special, infinitesimal value in the early universe in order to have the two densities nearly coincide today. Recently, we introduced the notio n of tracker fields to avoid this initial conditions problem. In the paper, we address the following questions: What is the general condition to have tracker fields? What is the relation between the matter energy density and the equation-of-state of the universe imposed by tracker solutions? And can tracker solutions help to explain why quintessence is becoming important t oday rather than during the early universe? [S0556-2821(99)05610-6].