Viability of Noether symmetry of F(R) theory of gravity

Sarkar, Kaushik; Sk., Nayem; Debnath, Subhra; Sanyal, Abhik Kumar

doi:10.48550/arxiv.1207.3219

Cited by 11 publications

(25 citation statements)

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“…For the case of classical and quantum cosmology, either Bianchi or higher derivatives, the first works known to us are [2], [3], [4], [5] and [6] (where conditional symmetries are used). Work on the subject has been recently revived, see [7], [8], [9] and [10]. The method essentially consists in applying the standard theory of variational symmetries [11], [12] to the Lagrangian of some minisuperspace model.…”

Section: Introductionmentioning

confidence: 99%

Conditional symmetries and the canonical quantization of constrained minisuperspace actions: The Schwarzschild case

Christodoulakis

Dimakis

Terzis

et al. 2013

Journal of Geometry and Physics

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A conditional symmetry is defined, in the phase-space of a quadratic in velocities constrained action, as a simultaneous conformal symmetry of the supermetric and the superpotential. It is proven that such a symmetry corresponds to a variational (Noether) symmetry.The use of these symmetries as quantum conditions on the wave-function entails a kind of selection rule. As an example, the minisuperspace model ensuing from a reduction of the Einstein -Hilbert action by considering static, spherically symmetric configurations and r as the independent dynamical variable, is canonically quantized. The conditional symmetries of this reduced action are used as supplementary conditions on the wave function. Their integrability conditions dictate, at a first stage, that only one of the three existing symmetries can be consistently imposed. At a second stage one is led to the unique Casimir invariant, which is the product of the remaining two, as the only possible second condition on Ψ. The uniqueness of the dynamical evolution implies the need to identify this quadratic integral of motion to the reparametrisation generator. This can be achieved by fixing a suitable parametrization of the r-lapse function, exploiting the freedom to arbitrarily rescale it. In this particular parametrization the measure is chosen to be the determinant of the supermetric. The solutions to the combined Wheeler -DeWitt and linear conditional symmetry equations are found and seen to depend on the product of the two "scale factors".

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Section: Introductionmentioning

confidence: 99%

Conditional symmetries and the canonical quantization of constrained minisuperspace actions: The Schwarzschild case

Christodoulakis

Dimakis

Terzis

et al. 2013

Journal of Geometry and Physics

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show abstract

“…In view of such exciting results, till date, there has been numerous attempts in this field. Of particular importance are its application in scalar-tensor theory of gravity [11,12,13] and in higher order theory of gravity [6,7,8,14,15,16,17,18,19,20,21,22,23,24]. F (R) theory of gravity, is a class of extended theories of gravity (ETGs) that represents one of the simplest modifications to GTR [25].…”

Section: Introductionmentioning

confidence: 99%

“…Results (metric formalism) in a nutshell are (i) Noether symmetry gives F (R) = F 0 R 3 2 along with a conserved current d dt (a √ R) in R-W metric when coupled to pressure-less dust or in vacuum [6,7,8,13]. (ii) It does not yield any symmetry when the configuration space is enlarged by including scalar field or in anisotropic model [22]. (iii) Inclusion of gauge term does not improve the situation [29,30,31].…”

Section: Introductionmentioning

confidence: 99%

“…(iii) Inclusion of gauge term does not improve the situation [29,30,31]. (iv) Exact solution in R-W metric does not satisfy all cosmological data and a linear term may be necessary in addition [22]. (v) Metric variation of higher order theory of gravity requires to fix the Ricci scalar in addition to the metric tensor at the boundary.…”

Section: Introductionmentioning

confidence: 99%

“…(vi) A non-Noether conserved current exists in general for gravity when a non-minimally coupled scalar field is added to F (R). It has been shown that it is useful to obtain improved exact solution [22,31].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Noether symmetry of Palatini F(ℜ) gravity

2018

Int. J. Geom. Methods Mod. Phys.

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In metric formalism, Noether symmetry of F(R) theory of gravity in vacuum and in the presence of pressureless dust yields F (R) ∝ R 3 2 along with the conserved current d dt (a √ R) in Robertson-Walker metric and nothing else. However, Roshan et.al. has claimed in Phys.Lett.B668, 238 (2008) [1] that Noether symmetry in the context of Palatini F (ℜ) theory of gravity admits F (ℜ) ∝ ℜ s , (where s is arbitrary) in matter domain era in Friedmann-Robertson-Walker universe. But, it has been shown that the conserved current obtained under the process does not satisfy the field equations in general. Here, it is shown that Noether Symmetry admits F (ℜ) ∝ ℜ 3 2 along with a conserved current Σ0a[ȧ a +Φ 2Φ ] in Palatini gravity. Thus, their claim is not right.

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Noether symmetry in f ( T ) teleparallel gravity

2017

Physics Letters B

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Noether symmetry in teleparallel f (T ) gravity, where T is the torsion scalar, has been studied in the background of Robertson-Walker space-time. It is found that Noether symmetry admits f (T ) ∝ T 3 2 and the associated conserved current is Σ = aȧT 1 2 , in matter dominated era. In the process, the recent claim by Wei et.al.[1] that Noether symmetry admits f (T ) ∝ T n , (where n is an arbitrary constant) is found not to be correct, since the conserved current satisfies the field equations only for a special choice of n = 3 2 . Further, correspondence between f (R) and f (T ) theories of gravity has also been established.

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Viability of Noether symmetry of F(R) theory of gravity

Cited by 11 publications

References 0 publications

Conditional symmetries and the canonical quantization of constrained minisuperspace actions: The Schwarzschild case

Conditional symmetries and the canonical quantization of constrained minisuperspace actions: The Schwarzschild case

Noether symmetry of Palatini F(ℜ) gravity

Noether symmetry in f ( T ) teleparallel gravity

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