2011 # Using the Noether symmetry approach to probe the nature of dark energy

**Abstract:** We propose to use a model-independent criterion based on first integrals of
motion, due to Noether symmetries of the equations of motion, in order to
classify the dark energy models in the context of scalar field (quintessence or
phantom) FLRW cosmologies. In general, the Noether symmetries play an important
role in physics because they can be used to simplify a given system of
differential equations as well as to determine the integrability of the system.
The Noether symmetries are computed for nine distinct …

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“…As discussed in [52], their existence allows to select physically observable universes and, specifically, to select analytical models related to observations. In particular, it is possible to classify dark energy behaviors related to Noether symmetries and then discriminate between physical and unphysical solutions (see [53,[67][68][69]). These topics will be the argument of a forthcoming, detailed study.…”

confidence: 99%

“…As discussed in [52], their existence allows to select physically observable universes and, specifically, to select analytical models related to observations. In particular, it is possible to classify dark energy behaviors related to Noether symmetries and then discriminate between physical and unphysical solutions (see [53,[67][68][69]). These topics will be the argument of a forthcoming, detailed study.…”

confidence: 99%

“…Finally, expanding the action up to second order, we found the condition for stability of the de Sitter solution and showed it to be an attractor of the system for 3H d S + q d S > 0 in all five cases. It deserves mentioning at this point that symmetries are not only a mathematical tool to solve dynamical systems but also bring about the opportunity to physically select an observable universe and "particularly" to single out analytical models related to observation [96] which would provide a tool to classify dark energy models related to Noether symmetry; see [97][98][99].…”

confidence: 99%

“…We would like to remark that the application of the complete Noether's theorem in scalar field cosmology can be found in 6 and the application of Lie point symmetries in, 7 hence the results of 1 are not new in the literature.…”

confidence: 99%