  We investigate a fourth order model of gravity, having a free length
parameter, and no cosmological constant or dark energy. We consider
cosmological evolution of a flat Friedmann universe in this model for the case
that the length parameter is of the order of present Hubble radius. By making a
suitable choice for the present value of the Hubble parameter, and value of
third derivative of the scale factor (the jerk) we find that the model can
explain cosmic acceleration to the same degree of accuracy as the standard
concordance model. If the free length parameter is assumed to be
time-dependent, and of the order of the Hubble parameter of the corresponding
epoch, the model can still explain cosmic acceleration, and provides a possible
resolution of the cosmic coincidence problem. We work out the effective
equation of state, and its time evolution, in our model. We also compare
redshift drift in our model, with that in the standard model. The equation of
state and the redshift drift serve to discriminate our model from the standard
model.
