Noether symmetry in f(R)f(R) cosmology

The Noether symmetry of a generic f(R)f(R) cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of f(R)f(R) for which such symmetries exist. It is shown that the resulting form of f(R)f(R) yields a power law expansion for the cosmological scale factor. We also obtain the effective equation of state parameter for the corresponding cosmology and show that our model can provide a gravitational alternative to the quintessence.