<i>f</i>(<i>R</i>) cosmology from Noether’s symmetry

Capozziello, Salvatore; Felice, Antonio De

doi:10.1088/1475-7516/2008/08/016

Cited by 198 publications

(221 citation statements)

References 61 publications

(110 reference statements)

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“…We mention here that this is an special class of solutions founded before in literature [61] (for the case of purely f (R, T ) = F (R) see [61]). The associated Noether charge reads:…”

Section: Noether Symmetry In F (R T ) Gravitymentioning

confidence: 89%

Cosmological viable mimetic f(R) and f(R, T) theories via Noether symmetry

Momeni

Myrzakulov

Güdekli

2015

Int. J. Geom. Methods Mod. Phys.

116

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Extended f(R) theories of gravity have been investigated from the symmetry point of view. We briefly has been investigated Noether symmetry of two types of extended f(R) theories: f(R, T) theory, in which curvature is coupled non-minimally to the trace of energy–momentum tensor Tμν and mimetic f(R) gravity, a theory with a scalar field degree of freedom, but ghost-free and with internal conformal symmetry. In both cases we write point-like Lagrangian for flat Friedmann–Lemaitre–Robertson–Walker (FLRW) cosmological background in the presence of ordinary matter. We have been shown that some classes of models existed with Noether symmetry in these viable extensions of f(R) gravity. As a motivated idea, we have been investigating the stability of the solutions and the bouncing and ΛCDM models using the Noether symmetries. We have been shown that in mimetic f(R) gravity bouncing and ΛCDM solutions are possible. Also a class of solutions with future singularities has been investigated.

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“…We mention here that this is an special class of solutions founded before in literature [61] (for the case of purely f (R, T ) = F (R) see [61]). The associated Noether charge reads:…”

Section: Noether Symmetry In F (R T ) Gravitymentioning

confidence: 89%

Cosmological viable mimetic f(R) and f(R, T) theories via Noether symmetry

Momeni

Myrzakulov

Güdekli

2015

Int. J. Geom. Methods Mod. Phys.

116

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“…Earlier attempts to find the Noether symmetry for ( ) theory of gravity in vacuum and matter dominated era lead to ( ) ∝ 3/2 [6][7][8][9][10][11][12][13]. Such a form is not suitable to explain presently available cosmological data [13].…”

Section: Discussionmentioning

confidence: 99%

“…In the process, it is possible to construct a point Lagrangian, and one can demand Noether symmetry to find a suitable form of ( ). Following this technique, several authors [6][7][8][9][10][11][12] have found ( ) ∝ 3/2 in the Robertson-Walker metric both in vacuum ( = = 0) and pressureless dust ( = 0). Although such a form of ( ) shows accelerating expansion in the matter dominated era ( = 0), nevertheless, early decelerating phase tracks as ∝ 1/2 in the matter dominated era instead of usual 2/3 and ∝ 4/3 in the radiation dominated era ( = /3) instead of usual 1/2 , creating problem in explaining structure formation [13].…”

Section: Introductionmentioning

confidence: 99%

Field Independent Cosmic Evolution

Sanyal

2013

Journal of Astrophysics

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It has been shown earlier that Noether symmetry does not admit a form of ( ) corresponding to an action in which ( ) is coupled to scalar-tensor theory of gravity or even for pure ( ) theory of gravity taking anisotropic model into account. Here, we prove that ( ) theory of gravity does not admit Noether symmetry even if it is coupled to tachyonic field and considering a gauge in addition. To handle such a theory, a general conserved current has been constructed under a condition which decouples higherorder curvature part from the field part. This condition, in principle, solves for the scale-factor independently. Thus, cosmological evolution remains independent of the form of the chosen field, whether it is a scalar or a tachyon.

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“…There are two kinds of Noether symmetry approach for cosmological studies in the literature : The first one is the so-called Noether symmetry approach in which the Lie derivative of a given Lagrangian vanishes, (Capozziello and de Ritis 1993;de Ritis et al 1990;Demianski et al 1 Sanyal and Modak 2001;Camci and Kucukakca 2007;Souza and Kremer 2008) and the second one is the so-called Noether gauge symmetry (NGS) approach Hussain et al 2011 We note that the Noether symmetry approach without gauge term allows one to choose the potential dynamically in the scalar-tensor gravity theory (Sanyal et al 2003), and very recently, the explicit form of the function f (R) (Capozziello and de Felice 2008;Vakili 2008). For this form of f (R), cosmological solutions of FRW metric can describe the accelerated period of the universe.…”

Section: Introductionmentioning

confidence: 99%

Noether gauge symmetry for f(R) gravity in Palatini formalism

Küçükakça

Camcı

2011

Astrophys Space Sci

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In this study, we consider a flat FriedmannRobertson-Walker (FRW) universe in the context of Palatini f (R) theory of gravity. Using the dynamical equivalence between f (R) gravity and scalar-tensor theories, we construct a point Lagrangian in the flat FRW spacetime. Applying Noether gauge symmetry approach for this f (R) Lagrangian we find out the form of f (R) and the exact solution for cosmic scale factor. It is shown that the resulting form of f (R) yield a powerlaw expansion for the scale factor of the universe.

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f(R) cosmology from Noether’s symmetry

Cited by 198 publications

References 61 publications

Cosmological viable mimetic f(R) and f(R, T) theories via Noether symmetry

Cosmological viable mimetic f(R) and f(R, T) theories via Noether symmetry

Field Independent Cosmic Evolution

Noether gauge symmetry for f(R) gravity in Palatini formalism

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