F(R) theory of gravity is claimed to admit a host of conserved currents under the imposition of Noether symmetry following various techniques. However, for a constrained system such as gravity, Noether symmetry is not on-shell. As a result, the symmetries do not necessarily satisfy the field equations in general, constraints in particular, unless the generator is modified to incorporate the constraints. In this paper, we apply the first theorem of Poisson to unveil the fact that not all the conserved currents appearing in the literature for F(R) theory of gravity satisfy the field equations. We also provide a list of available forms of F(R) along with associated conserved currents and construct a generalized action, which might address the cosmic puzzle, elegantly.

中文翻译：

---

分析 F(R) 引力理论中的守恒流

F(R)据称，重力理论在遵循各种技术的诺特对称性强加下承认了许多守恒电流。然而，对于一个受约束的系统，例如重力，Noether 对称性不是壳上的。因此，对称性通常不一定满足场方程，特别是约束，除非修改生成器以包含约束。在本文中，我们应用泊松第一定理来揭示一个事实，即并非所有文献中出现的守恒电流F(R)引力理论满足场方程。我们还提供了可用形式的列表F(R)连同相关的守恒电流并构建一个广义的动作，这可能会优雅地解决宇宙难题。