Singularity problem in f(R) model with non-minimal coupling

TL;DR

This paper investigates how non-minimal matter-geometry coupling in f(R) gravity can address singularities and dark energy oscillations, proposing specific coupling forms that improve early universe behavior and aligning cosmic evolution with standard models.

Contribution

It introduces a new scalar and stability condition in non-minimal f(R) gravity, analyzing oscillation behavior and singularity solutions, with numerical verification and constraints on coupling forms.

Findings

Logarithmic coupling improves singularity issues in early universe

Oscillating frequency matches theoretical predictions in numerical simulations

Cosmic evolution closely resembles standard f(R) models when coupling parameter exceeds 4

Abstract

We consider the non-minimal coupling between matter and the geometry in the f(R) theory. In the new theory which we established, a new scalar $\psi$ has been defined and we give it a certain stability condition. We intend to take a closer look at the dark energy oscillating behavior in the de-Sitter universe and the matter era, from which we derive the oscillating frequency, and the oscillating condition. More importantly, we present the condition of coupling form that the singularity can be solved. We discuss several specific coupling forms, and find logarithmic coupling with an oscillating period $\Delta T\sim\Delta z$ in the matter era $z>4$, can improve singularity in the early universe. The result of numerical calculation verifies our theoretic calculation about the oscillating frequency. Considering two toy models, we find the cosmic evolution in the coupling model is nearly the same as that in the normal f(R) theory when $lna>4$. We also discuss the local tests of the non-minimal coupling f(R) model, and show the constraint on the coupling form.