We study Palatini f (R) cosmology using Noether symmetry approach for the matter-dominated universe. In order to construct a point-like Lagrangian in the flat FRW space–time, we use the dynamical equivalence between f (R) gravity and scalar–tensor theories. The existence of Noether symmetry of the cosmological f (R) Lagrangian helps us to find out the form of f (R) and the exact solutions for cosmic scale factor. We show that this symmetry always exist for f (R) ∼ Rn and the Noether constant is a function of the Newton’s gravitational constant and the current matter content of the universe.

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