Reconstruction of f (R) Lagrangian from a massive scalar field

Abstract

A reconstruction scheme from a minimally coupled self-interacting scalar field is discussed in the regime of f (R) gravity. This involves a direct way to solve the system of equations for some well-known form of self-interaction potential. For a power law or combination of power law potential, the scheme originates from a theorem of invertible point transformation and integrability of anharmonic oscillator equations. A case with exponential self-interaction potential is also included. The viability of the f (R) models is discussed in brief.