Deep connection between f(R) gravity and the interacting dark sector model

TL;DR

This paper explores the deep theoretical link between f(R) gravity and interacting dark sector models, showing how conformal transformations relate to mass dilation and influence energy flow, with implications for cosmological observations.

Contribution

It constructs f(R) gravity in terms of mass dilation in the Einstein frame and links it to interacting dark sector models, providing insights into the coincidence problem.

Findings

Energy flow from dark energy to dark matter is ensured by observationally consistent f(R) models.

Conformal transformation corresponds to mass dilation, affecting dark sector interactions.

The approach offers a new perspective on the coincidence problem in cosmology.

Abstract

We examine the conformal equivalence between the $f(R)$ gravity and the interacting dark sector model. We review the well-known result that the conformal transformation physically corresponds to the mass dilation which marks the strength of interaction between dark sectors. Instead of modeling f(R) gravity in the Jordan frame, we construct the $f(R)$ gravity in terms of mass dilation function in the Einstein frame. We find that the condition to keep $f(R)$ gravity consistent with CMB observations ensures the energy flow from dark energy to dark matter in the corresponding interacting model, which meets the requirement to alleviate the coincidence problem in the Einstein framework.