Vacuum Solution of a Linear Red-Shift Based Correction in $f(R)$ Gravity

TL;DR

This paper explores a linear red-shift based correction in vacuum $f(R)$ gravity, showing it can account for late-time cosmic acceleration without dark energy and reduces to de Sitter universe without correction.

Contribution

It introduces a specific linear correction in $f(R)$ gravity and analyzes its implications for late-time acceleration and asymptotic behavior.

Findings

Linear correction can explain late-time acceleration without dark energy.

Solutions tend to de Sitter universe when correction is absent.

Asymptotic action for the correction is calculated.

Abstract

In this paper we have considered a red-shift based linear correction in derivative of action in the context of vacuum $f(R)$ gravity. Here we have found out that the linear correction may describe the late time acceleration which is appeared by SNeIa with no need of dark energy. Also we have calculated the asymptotic action for the desired correction. The value of all solutions may reduce to de' Sitter universe in the absence of correction term.