Exponential Potentials and Attractor Solution of Dilatonic Cosmology

TL;DR

This paper explores a scalar-tensor cosmological model with exponential potential, analyzing its critical points, attractor behavior, and compatibility with current observations, concluding that the universe's acceleration is not its final stage.

Contribution

It provides a detailed analysis of the attractor solutions in dilatonic cosmology with exponential potentials, including numerical phase plane plots and observational constraints.

Findings

Critical points can be attractors under certain parameter conditions.

The model's parameters can produce cosmological evolution consistent with observations.

The current accelerating universe is not predicted to be the final stage.

Abstract

We present the scalar-tensor gravitational theory with an exponential potential in which pauli metric is regarded as the physical space-time metric. We show that it is essentially equivalent to coupled quintessence(CQ) model. However for baryotropic fluid being radiation there are in fact no coupling between dilatonic scalar field and radiation. We present the critical points for baryotropic fluid and investigate the properties of critical points when the baryotropic matter is specified to ordinary matter. It is possible for all the critical points to be attractors as long as the parameters $\lambda$ and $\beta$ satisfy certain conditions. To demonstrate the attractor behaviors of these critical points, We numerically plot the phase plane for each critical point. Finally with the bound on $\beta$ from the observation and the fact that our universe is undergoing an accelerating expansion, we conclude that present accelerating expansion is not the eventual stage of universe. Moreover, we numerically describe the evolution of the density parameters $\Omega$ and the decelerating factor $q$, and computer the present values of some cosmological parameters, which are consistent with current observational data.