We study the cosmological evolution of a scalar field that couples to the trace ${T=T}_a^a$ of the energy momentum tensor of all the fields (including itself). In the case of a shallow exponential potential, the presence of coupling to the trace T in the field equation makes the energy density of the scalar field decrease faster, thereby hastening the commencement of radiation domination. This effect gradually diminishes at later epochs, allowing the scalar field to dominate the energy density again. We interpret this phase as the current epoch of cosmic acceleration with ${\Omega }_{\phi }=\mathrm{0.7.}\mathrm{}$ A variant of this model can lead to accelerated expansion at the present epoch, followed by an $a\left(t\right)\mathrm{}\propto t^{2/3}$ behavior as $\overrightarrow{t}\infty ,$ making the model free from a future event horizon. The main features of the model are independent of initial conditions. However, fine-tuning of parameters is necessary for viable evolution.

• Received 1 January 2003
• Publisher error corrected 12 May 2003

DOI:https://doi.org/10.1103/PhysRevD.67.083509