Scalarons mimicking Dark Matter in the Hu-Sawicki model of f(R) gravity

TL;DR

This paper investigates the scalar field derived from the Hu-Sawicki f(R) gravity model, demonstrating its potential as a dark matter candidate due to its chameleonic properties and mass evolution over cosmic time.

Contribution

It provides a detailed analysis of the scalaron in the Hu-Sawicki model, showing its chameleonic behavior and viability as a dark matter candidate, including its mass evolution with redshift.

Findings

Scalaron exhibits chameleonic behavior, becoming light in low-density regions.

Scalaron mass is close to ultralight axion dark matter.

Scalaron mass decreases with the expansion of the universe.

Abstract

In this paper, we conduct a study on the scalar field obtained from $\mathit{f(R)}$ gravity via Weyl transformation of the spacetime metric $g_{\mu\nu}$ from the Jordan frame to the Einstein frame. The scalar field is obtained as a result of the modification in the geometrical part of Einstein's field equation of General Relativity. For the Hu-Sawicki model of $\mathit{f(R)}$ gravity, we find the effective potential of the scalar field and calculate its mass. Our study shows that the scalar field (also named as scalaron) obtained from this model has the chameleonic property, i.e.\ the scalaron becomes light in the low-density region while it becomes heavy in the high-density region of matter. Then it is found that the scalaron can be regarded as a dark matter (DM) candidate since the scalaron mass is found to be quite close to the mass of ultralight axions, a prime DM candidate. Thus the scalaron in the Hu-Sawicki model of $\mathit{f(R)}$ gravity behaves as DM. Further, a study on the evolution of the scalaron mass with the redshift is also carried out, which depicts that scalaron becomes light with expansion of the Universe and with different rates at different stages of the Universe.