Classification of scalar field potentials with cosmological scaling solutions

1998/09/22 by Andrew R. Liddle, Andrew R Liddle, Robert J. Scherrer +1 · 32 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #astro-ph #gr-qc #hep-ph

paper · pdf · doi:10.1103/physrevd.59.023509

published as Phys.Rev.D59:023509,1999 · 8 pages RevTeX file with four figures incorporated (uses RevTeX and epsf)

arxiv created 1998/09/22 · openalex publication_date 1998/12/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

Citations

• Cosmological consequences of a rolling homogeneous scalar field

Cited by

• Observational constraints on the braneworld model with branebulk energy exchange
• General analytic formulas for attractor solutions of scalar-field dark energy models and their multifield generalizations
• Stability of multifield cosmological solutions
• Homogeneous scalar field and the wet dark sides of the universe
• Exploring parameter constraints on quintessential dark energy: The inverse power law model
• CONSTRAINTS ON DARK ENERGY FROM THE OBSERVED EXPANSION OF OUR COSMIC HORIZON
• On the potentials yielding cosmological scaling solutions
• Constraints on linear negative potentials in quintessence and phantom models from recent supernova data
• Multiple kinetic k-essence, phantom barrier crossing and stability
• Kinetically driven quintessence
• Dynamics of assisted quintessence
• The quintom model with O(N) symmetry
• Analysis of Two Quintessence Models with Type Ia Supernova Data
• Some constraints on inflation models with power-law potentials
• Limits on dark radiation, early dark energy, and relativistic degrees of freedom
• Phantom dark energy, cosmic doomsday, and the coincidence problem
• Scalar field cosmological models with finite scale factor singularities
• Interacting three fluid system and thermodynamics of the universe bounded by the event horizon
• Dark radiation as a signature of dark energy
• Old dark energy
• The cosmological constant and dark energy
• Gravitational collapse with tachyon field and barotropic fluid
• A new extended quintessence
• Undermining the cosmological principle: almost isotropic observations in inhomogeneous cosmologies
• Search for tracker potentials in quintessence theory
• Two-scalar model for a small but nonzero cosmological constant
• Dark Energy from structure: a status report
• The Cosmological Constant
• Variable G Corrections to Statefinder Parameters of Dark Energy
• Big bang nucleosynthesis and CMB constraints on dark energy
• Phantom cosmologies
• Genesis of cosmological tracker fields