2011 # Constraints and analytical solutions off ( R ) theories of gravity using Noether symmetries

**Abstract:** We perform a detailed study of the modified gravity f (R) models in the light of the basic geometrical symmetries, namely Lie and Noether point symmetries, which serve to illustrate the phenomenological viability of the modified gravity paradigm as a serious alternative to the traditional scalar field approaches. In particular, we utilize a model-independent selection rule based on first integrals, due to Noether symmetries of the equations of motion, in order to identify the viability of f (R) models in the c…

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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%

“…The existence of Gödel, Einstein and de Sitter universes in modified gravity theories was studied in [49] whereas analytical solutions for spherically symmetric systems were found in [50,51]. Methods of finding analytical solutions of f (R) theories using Noether symmetries were presented in [52].…”

confidence: 99%

“…The latter implies that in the configuration space (minisuperspace), the first integrals are considered as "selection rules" for scalar field potentials and coupling functions in the case of modified gravity theories. The above features have inspired many authors to propose the admittance of a Noether (point or dynamical) symmetry by the field equations as a selection rule for dark-energy models, including those of modified gravity [8][9][10][11][12][13][14][15][16][17][18][19].…”

confidence: 99%