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We propose to use dynamical symmetries of the field equations, in order to classify the dark energy models in the context of scalar field (quintessence or phantom) Friedmann-Lema\^tre-Robertson Walker cosmologies. Practically, symmetries provide a useful mathematical tool in physical problems since they can be used to simplify a given system of differential equations as well as to determine the integrability of the physical system. The requirement that the field equations admit dynamical symmetries results in two potentials, one of which is the well-known unified dark matter potential and another new potential. For each hyperbolic potential we obtain the corresponding analytic solution of the field equations. The proposed analysis suggests that the requirement of the contact symmetry appears to be very competitive to other independent tests used to probe the functional form of a given potential and thus the associated nature of dark energy. Finally, in order to test the viability of the above scalar field models we perform a joint likelihood analysis using some of the latest cosmological data.
Paliathanasis et al. (Wed,) studied this question.