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

Abstract

Canonization of F(R) theory of gravity to explore Noether symmetry is performed treating R - 6(\frac{\ddot a}{a} + \frac{\dot a^2}{a^2} + \frac{k}{a^2}) = 0 as a constraint of the theory in Robertson-Walker space-time, which implies that R is taken as an auxiliary variable. Although it yields correct field equations, Noether symmetry does not allow linear term in the action, and as such does not produce a viable cosmological model. Here, we show that this technique of exploring Noether symmetry does not allow even a non-linear form of F(R), if the configuration space is enlarged by including a scalar field in addition, or taking anisotropic models into account. Surprisingly enough, it does not reproduce the symmetry that already exists in the literature (A. K. Sanyal, B. Modak, C. Rubano and E. Piedipalumbo, Gen.Relativ.Grav.37, 407 (2005), arXiv:astro-ph/0310610) for scalar tensor theory of gravity in the presence of R^2 term. Thus, R can not be treated as an auxiliary variable and hence Noether symmetry of arbitrary form of F(R) theory of gravity remains obscure. However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar-tensor theory (A. K. Sanyal, Phys.Lett.B624, 81 (2005), arXiv:hep-th/0504021 and Mod.Phys.Lett.A25, 2667 (2010), arXiv:0910.2385 [astro-ph.CO]). Here, we briefly expatiate the non-Noether conserved current and cite an example to reveal its importance in finding cosmological solution for such an action, taking F(R) \propto R^{3/2}.

16 pages, 1 figure. appears in Int J Theoretical Phys (2012)

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• Noether Symmetries of a Modified Model in Teleparallel Gravity and a New Approach for Exact Solutions
• On the equivalence between different canonical forms of F(R) theory of gravity
• A viable form of the metric Teleparallel F(T) theory of gravity
• Degenerate Hamiltonian operator in higher-order canonical gravity -- the problem and a remedy
• Late-time-accelerated expansion arisen from gauge fields in an anisotropic background and a fruitful trick for Noether's approach
• Constraints on cosmological parameters in light of the scalar-tensor theory of gravity and swampland conjectures
• The Isotopic Field-Charge Assumption Applied to the Electromagnetic Interaction
• Quantum cosmology of Bianchi VIII, IX LRS geometries
• Electromagnetic Interaction in the Presence of Isotopic Field-Charges and a Kinetic Field
• Reconstructing modified and alternative theories of gravity
• Validating variational principle for higher order theory of gravity
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