Scalar field with the source in the form of the stress-energy tensor   trace as a dark energy model
  We consider a scalar-tensor theory of gravitation with the scalar source being the trace of the stress-energy tensor of the scalar field itself and matter. We obtain an example of a numerical solution of the cosmological equations which shows that under some special choice of the scalar parameters, there exists a slow-roll regime in which the modern values of the Hubble and deceleration parameters may be obtained. 
I. G. Dudko, Yu. P. Vyblyi
gr-qc