The Coincidence Problem in Holographic f(R) Gravity

TL;DR

This paper investigates the holographic principle in $f(R)$ gravity models, demonstrating that in Einstein frame, the ratio of dark matter to dark energy remains constant in a flat universe, revealing insights into cosmic coincidence.

Contribution

It applies the holographic principle to $f(R)$ gravity models in Einstein frame, showing the constant energy density ratio in a flat universe, which is a novel insight.

Findings

The energy density ratio of dark matter to dark energy is constant in Einstein frame.

Holographic principle applied to $f(R)$ models yields new cosmological insights.

The model supports a stable coincidence solution in flat universe scenarios.

Abstract

It is well-known that $f(R)$ gravity models formulated in Einstein conformal frame are equivalent to Einstein gravity together with a minimally coupled scalar field. In this case, the scalar field couples with the matter sector and the coupling term is given by the conformal factor. We apply the holographic principle to such interacting models. In a spatially flat universe, we show that the Einstein frame representation of $f(R)$ models leads to a constant ratio of energy densities of dark matter to dark energy.