English

Noether Symmetry of Palatini $F(\Re)$ gravity

General Relativity and Quantum Cosmology 2017-11-06 v4

Abstract

In metric formalism, Noether symmetry of F(R) theory of gravity in vacuum and in the presence of pressureless dust yields F(R)R32F(R)\propto R^\frac{3}{2} along with the conserved current ddt(aR)\frac{d}{dt} (a\sqrt R) in Robertson-Walker metric and nothing else. However, Roshan et.al. had claimed in Phys.Lett.B668,238(2008)\mathrm{Phys. Lett. \textbf{B668}, 238 (2008)} \cite{o} that Noether symmetry in the context of Palatini F()F(\Re) theory of gravity admits F()sF(\Re)\propto \Re^{s}, (where ss is an arbitrary constant) 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()32F(\Re)\propto\Re^\frac{3}{2} along with a conserved current Σ0a[a˙a+Φ˙2Φ]\Sigma_{0} {a}[\frac{\dot a}{a}+ \frac{\dot\Phi}{2\Phi}] in Palatini gravity. Thus, their claim is not right.

Keywords

Cite

@article{arxiv.1610.07445,
  title  = {Noether Symmetry of Palatini $F(\Re)$ gravity},
  author = {Nayem Sk},
  journal= {arXiv preprint arXiv:1610.07445},
  year   = {2017}
}

Comments

5 pages, Appear in International Journal of Geometric Methods in Modern Physics (IJGMMP)