A note on accelerating cosmologies from compactifications and S-branes

Abstract

We give a simple interpretation of the recent solutions for cosmologies with a transient accelerating phase obtained from compactification in hyperbolic manifolds, or from S-brane solutions of string/M-theory. In the four-dimensional picture, these solutions correspond to bouncing the radion field off its exponential potential. Acceleration occurs at the turning point, when the radion stops and the potential energy momentarily dominates. The virtues and limitations of these approaches become quite transparent in this interpretation.

Figures (1)

• Figure 1: Motion of the radion $\psi$ in the potential $V(\psi)$. In the left figure all the exponentials in the potential are positive. The field starts out at $\psi\to+\infty$ with very large (infinite) kinetic energy. Around the point where it turns around, the energy is potential-dominated and acceleration occurs. In the right figure there is a combination of a positive exponential (coming from four-form flux) and a negative exponential (from spherical compactification). We show two trajectories: one reaches $V(\psi)>0$ and hence produces positive acceleration (although the universe may be expanding or collapsing). The other turns around at $V=0$ and therefore does not lead to acceleration. All these possibilities are realized in the solutions described in the text. The asymptotic future behavior is determined by the attractor solutions of each potential.