2011
DOI: 10.1103/physrevd.83.103512
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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 … Show more

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Cited by 146 publications
(154 citation statements)
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References 97 publications
(128 reference statements)
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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.…”
Section: Discussionmentioning
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.…”
Section: Discussionmentioning
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].…”
Section: Discussionmentioning
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.…”
Section: Inmentioning
confidence: 99%