Reconstruction of $f(R)$ lagrangian from a massive scalar field

TL;DR

This paper reconstructs $f(R)$ gravity models using a minimally coupled massive scalar field, employing a novel theorem based on invertible point transformations to solve the field equations and analyze cosmological viability.

Contribution

It introduces a method using invertible point transformations to reconstruct $f(R)$ Lagrangians from scalar field models, including cases beyond the theorem's regime.

Findings

Reconstructed specific $f(R)$ models compatible with cosmological data.

Applied the method to well-known scalar potentials, demonstrating its effectiveness.

Discussed viability issues of the reconstructed models in light of observations.

Abstract

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.