Exponential potentials and cosmological scaling solutions

Copeland, Edmund J.; Liddle, Andrew R; Wands, David

doi:10.1103/PhysRevD.57.4686

Exponential potentials and cosmological scaling solutions

Nov, 1997

6 pages

Published in:

Phys.Rev.D 57 (1998) 4686-4690

e-Print:

gr-qc/9711068 [gr-qc]

DOI:

10.1103/PhysRevD.57.4686

Report number:

SUSX-TH-97-022,
SUSSEX-AST-97-11-1,
PU-RCG-97-20

View in:

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Abstract: (arXiv)

We present a phase-plane analysis of cosmologies containing a barotropic fluid with equation of state

p_\gamma = (\gamma-1) \rho_\gamma

, plus a scalar field

\phi

with an exponential potential

V \propto \exp(-\lambda \kappa \phi)

where

\kappa^2 = 8\pi G

. In addition to the well-known inflationary solutions for

\lambda^2 < 2

, there exist scaling solutions when

\lambda^2 > 3\gamma

in which the scalar field energy density tracks that of the barotropic 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(\phi)/\rho_\gamma \to 0

at late times, are always unstable (except for the cosmological constant case

\gamma = 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

\lambda^2 > 20

. We show that standard inflation models are unable to solve this `relic density' problem.

cosmological model
field theory: scalar
scaling
model: fluid
energy: density
potential
critical phenomena
inflation
numerical calculations

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