Abstract
We present a phase-plane analysis of cosmologies containing a baryotropic fluid with an equation of state plus a scalar field with an exponential potential where . In addition to the well-known inflationary solutions for , there exist scaling solutions when in which the scalar field energy density tracks that of the baryotropic fluid (which for example might be radiation or dust). We show that the scaling solutions are the unique late-time attractors whenever they exist. The fluid-dominated solutions, where at late times, are always unstable (except for the cosmological constant case . The relative energy density of the fluid and scalar field depends on the steepness of the exponential potential, which is constrained by nucleosynthesis to . We show that standard inflation models are unable to solve this “relic density” problem.
- Received 24 November 1997
DOI:https://doi.org/10.1103/PhysRevD.57.4686
©1998 American Physical Society