Stability of the scale parameter: Hu-Sawicki model

TL;DR

This paper investigates the stability of the scale parameter in the Hu-Sawicki model, revealing issues with physical evolution, suggesting modifications for stability, and questioning the model's physicality due to oscillatory behavior, but it was withdrawn due to a critical error.

Contribution

It introduces an analysis of the stability of the Hu-Sawicki model's scale parameter and explores modifications to improve stability and physical plausibility.

Findings

Physically meaningful evolution area is non-existent without modifications.

Adding a R^2 term enhances stability and aligns with phantom models.

Oscillatory behavior questions the physicality and observational reliability of the model.

Abstract

The evolution of the scale parameter in the Hu-Sawicki model is examined. We search the parameter area for instabilities. It turns out the parameter area of physically meaningful evolution is non-existent. For greater stability a stabilising term such as R^2 should be added. With the addition, the area mainly coincides with phantom models. We also find that the evolution of the scale parameter can be examined through a linear expansion and not only in the Hu-Sawicki case. The oscillatory behaviour found in the evolution raises questions of the physicality of the model. The behaviour can also cause current observations of the Hubble parameter to be misleading. This paper has been withdrawn by the authords due to a critical error in equation (10)