We study the cosmological evolution of a scalar field that couples to the trace T = T ^ { a } _ { a } of 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 } = 0.7 .
A variant of this model can lead to accelerated expansion at the present epoch followed by a a ( t ) \propto t ^ { 2 / 3 } behaviour as t \to \infty , making the model free from future event horizon .
The main features of the model are independent of initial conditions .
However , fine tuning of parameters is necessary for viable evolution .