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The aim of the present work is to investigate a non-minimally coupled scalarfield model through the Noether symmetry approach, with the radiation, matterand cosmological constant eras being analyzed. The Noether symmetry conditionallows a conformal coupling and by means of a change of coordinates in theconfiguration space the field equations can be reduced to a single equation,which is of the form of the Friedmann equation for the $\Lambda$CDM model. Inthis way, it is formally shown that the dynamical system can furnish solutionswith the same form as those of the $\Lambda$CDM model, although the theory hereconsidered is physically different from the former. The conserved quantityassociated with the Noether symmetry can be related to the kinetic term of thescalar field and could constrain the possible deviations of the model from the$\Lambda$CDM picture. Observational constraints on the variation of thegravitational constant can be imposed on the model through the initialcondition of the scalar field.

Conformal coupling associated with the Noether symmetry and its connection with the $\Lambda$CDM dynamics