Generalized Chaplygin Gas in a modified gravity approach

We study the generalized Chaplygin gas (GCG) scenario in a modified gravity approach. That is, we impose that our universe has a pure dust configuration, and allow for a modification of gravity that yields a GCG specific scale factor evolution. Moreover, assuming that this new hypothetical gravity theory obeys a generalization of Birkhoff's law, we determine the Schwarzschild-like metric in this new modified gravity. We also study the large scale structure formation in this model. Both the linear and non-linear growth are studied together with the growth of the velocity fluctuation in the linear perturbation theory. We compare our results with those corresponding to the $\Lambda$CDM model and discuss possible distinguishable features.