We study flat Friedmann–Robertson–Walker models with a perfect fluid matter source and a scalar field nonminimally coupled to matter having a double exponential potential. It is shown that the scalar field almost always diverges to infinity. Under conditions on the parameter space, we show that the model is able to give an acceptable cosmological history of our Universe, that is, a transient matter era followed by an accelerating future attractor. It is found that only a very weak coupling can lead to viable cosmology. We study in the Einstein frame the cosmological viability of the asymptotic form of a class of $f(R)$ theories predicting acceleration. The role of the coupling constant is briefly discussed.

• Received 4 January 2014
• Publisher error corrected 3 June 2014

DOI:https://doi.org/10.1103/PhysRevD.89.103540