Attractor behavior in dilatonic (phantom) dark energy model with an especial potential

Abstract

The dilaton in Weyl-Scale induced gravitational theory is regarded as a candidate of dark energy. When the potential of dilaton field is taken as the form \( W_\sigma + \sigma ^2 e^{ - \beta \sigma ^2 } \), that there exist attractor solutions to the canonical dilatonic dark energy model and the phontam model, and these attractors correspond to an equation of state ω = −1 and a cosmic density parameter Ωσ = 1, which are important features for a dark energy model and can fit with the current observations. We find a sufficient condition of the existence of a late time de Sitter attractor. The attractor behaviors, the evolutions of the state parameter ω and the cosmic density parameter Ω, the evolution of X\( \left( {\tfrac{\sigma } {{\sigma _0 }}} \right) \) and Y\( \left( {\tfrac{{\dot \sigma }} {{\sigma _0^2 }}} \right) \) with respect to N(ln a) are shown numerically.