Study of symmetry in F(R) theory of gravity

Understand

An action in which the Ricci scalar is nonminimally coupled with a scalar field and contains higher order curvature invariant terms carries a conserved current under certain conditions that decouples geometric part from the scalar field.

• The conserved current relates the pair of arbitrary coupling parameters $f(\phi)$ and $\omega(\phi)$ with the gravitational field variable, where $\omega(\phi)$ is the Brans-Dicke coupling parameter.
• The existence of such conserved current may be helpful to sketch the cosmological evolution from its early age till date in a single frame.