On the LCDM Universe in f(R) gravity

TL;DR

This paper investigates f(R) gravity models capable of reproducing the LCDM expansion history, concluding that only standard General Relativity with a positive cosmological constant naturally achieves this without extra matter degrees of freedom.

Contribution

It demonstrates that only General Relativity with a positive cosmological constant can exactly reproduce LCDM expansion in f(R) gravity, highlighting the uniqueness of this solution.

Findings

Only GR with positive Lambda admits exact LCDM expansion in f(R) models.

More general f(R) functions require additional matter degrees of freedom.

Explicit reconstructions of f(R) consistent with the LCDM expansion are provided.

Abstract

Several different explicit reconstructions of f(R) gravity are obtained from the background FRW expansion history. It is shown that the only theory whose Lagrangian is a simple function of the Ricci scalar R, that admits an exact LCDM expansion history is standard General Relativity with a positive cosmological constant and the only way to obtain this behaviour of the scale factor for more general functions of R is to add additional degrees of freedom to the matter sector.