Revisiting f(R) gravity models that reproduce $\Lambda$CDM expansion

TL;DR

This paper reconstructs an $f(R)$ gravity model that exactly reproduces the $ ext{Lambda}$CDM expansion history, providing analytical forms valid from early universe to late acceleration, and confirms its viability without future singularities.

Contribution

It presents a new analytical $f(R)$ gravity model matching $ ext{Lambda}$CDM evolution and demonstrates its physical viability across cosmic history.

Findings

Analytical $f(R)$ form reproduces $ ext{Lambda}$CDM expansion.

Model is viable for early and late universe.

No future singularities in the model.

Abstract

We reconstruct an $f(R)$ gravity model that gives rise to the particular $\Lambda$CDM background evolution of the universe. We find well-defined, real-valued analytical forms for the $f(R)$ model to describe the universe both in the early epoch from the radiation to matter dominated eras and the late time acceleration period. We further examine the viability of the derived $f(R)$ model and find that it is viable to describe the evolution of the universe in the past and there does not exist the future singularity in the Lagrangian.