Study of symmetry in F(R) theory of gravity
  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.
