Reconstruction of $f(R)$ lagrangian from a massive scalar field
  We present a reconstruction of the Lagrangian for $f(R)$ gravity by using a
massive scalar field. The scalar field is minimally coupled to the action of
$f(R)$ gravity. We demonstrate the use of a theorem based on invertible point
transformation of anharmonic oscillator equation that has only recently been
applied to gravitational physics. This avenue gives us a direct way to solve
the field equations for a few well-known self-interaction potential of the
scalar field. A few cases which do not fall in the regime of the theorem are
also discussed. The $f(R)$ models are discussed in the context of recent
cosmological observations and viability issues.
