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We analyse a scalar field non-minimally coupled to gravity in the context ofa Universe described by the flat Friedmann-Robertson-Walker (F-R-W) metric. Theadopted model comprises a Universe filled by the scalar field and standardmatter (dark and baryonic). The corresponding field equations are obtainedthrough the Palatini formalism. From the action of the model in the flat F-R-Wspace-time, a point-like Lagrangian of first order is obtained and the Noethersymmetry approach is applied to restrict the forms of the a priori undefinedcoupling and potential of the scalar field. We show that the massive scalarfield is associated with a Noether symmetry of the model. Analyticalcosmological solutions for this case are found and their respective importancefor the description of the dark energy are discussed.

Analysis of the non-minimally coupled scalar field in the Palatini formalism by the Noether symmetry approach