Stability of the scale parameter: Hu-Sawicki model

Abstract

The evolution of the scale parameter in the Hu-Sawicki model is examined. We search the parameter area for instabilities. It turns out the parameter area of physically meaningful evolution is non-existent. For greater stability a stabilising term such as R^2 should be added. With the addition, the area mainly coincides with phantom models. We also find that the evolution of the scale parameter can be examined through a linear expansion and not only in the Hu-Sawicki case. The oscillatory behaviour found in the evolution raises questions of the physicality of the model. The behaviour can also cause current observations of the Hubble parameter to be misleading. This paper has been withdrawn by the authords due to a critical error in equation (10)