What question did this study set out to answer?

To analyze cosmologies with baryotropic fluids and scalar fields featuring exponential potentials and identify late-time attractors.

April 15, 1998Open Access

Exponential potentials and cosmological scaling solutions

Key Points

To analyze cosmologies with baryotropic fluids and scalar fields featuring exponential potentials and identify late-time attractors.
Conducted phase-plane analysis of cosmologies with a baryotropic fluid and a scalar field with exponential potential.
Investigated conditions for scaling solutions and their stability based on energy densities.
Evaluated the implications of steepness of potential related to nucleosynthesis constraints.
Identified unique late-time attractors in scaling solutions for certain conditions (${\lambda}^{2}>3{\gamma}$).
Found fluid-dominated solutions are unstable, particularly when ${\lambda}^{2}<20$.
Demonstrated that standard inflation models cannot resolve the relic density problem.

Abstract

We present a phase-plane analysis of cosmologies containing a baryotropic fluid with an equation of state p_= (-1) _, plus a scalar field with an exponential potential V (-) where ^2=8. In addition to the well-known inflationary solutions for ^23 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 V () /_0 at late times, are always unstable (except for the cosmological constant case =0). The relative energy density of the fluid and scalar field depends on the steepness of the exponential potential, which is constrained by nucleosynthesis to ^2>20. We show that standard inflation models are unable to solve this ``relic density'' problem.

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