  We explore the scalar field obtained under the conformal transformation of
the spacetime metric $g_{\mu\nu}$ from the Jordan frame to the Einstein frame
in $f(R)$ gravity. This scalar field is the result of the modification in the
gravitational part of the Einstein's general relativistic theory of gravity.
For $f(R)=\frac{R^{1+\delta}}{R_{c}^{\delta}}$, we find the effective potential
of the scalar field and calculate the mass of the scalar field particle
"scalaron". It is shown that the mass of the scalaron depends upon the energy
density of standard matter in the background. The interaction between standard
matter and scalaron is weak in the high curvature regime. This linkage between
the mass of the scalaron and the background leads to the physical effects of
dark matter and is expected to reflect the anisotropic propagation of scalaron
in moving baryonic matter fields as in merging clusters (Bullet cluster, the
Abell 520 system, MACS etc.). Such scenario also satisfies the local gravity
constraints of $f(R)$ gravity. We further calculate the equation of state of
the scalar field in the action-angle variable formalism and show its distinct
features as the dark matter and dark energy with respect to energy density of
the scalar field at different values of the model parameter $\delta$.
