Cosmic acceleration in a model of fourth order gravity

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 the present Hubble radius. By making a suitable choice for the present value of the Hubble parameter, and the value of the 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. The fourth order correction terms are proportional to the metric, and hence mimic the cosmological constant. 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.