An attractive method of obtaining an effective cosmological constant at the
present epoch is through the potential energy of a scalar field. Considering
models with a perfect fluid and a scalar field, we classify all potentials for
which the scalar field energy density scales as a power-law of the scale factor
when the perfect fluid density dominates. There are three possibilities. The
first two are well known; the much-investigated exponential potentials have the
scalar field mimicking the evolution of the perfect fluid, while for negative
power-laws, introduced by Ratra and Peebles, the scalar field density grows
relative to that of the fluid. The third possibility is a new one, where the
potential is a positive power-law and the scalar field energy density decays
relative to the perfect fluid. We provide a complete analysis of exact
solutions and their stability properties, and investigate a range of possible
cosmological applications.Comment: 8 pages RevTeX file with four figures incorporated (uses RevTeX and
epsf
