Early dark energy in $k$-essence

TL;DR

This paper explores a new $k$-essence-based early dark energy model that aims to address the coincidence problem by linking EDE onset and end to the radiation-matter transition, but finds limitations in fully realizing this scenario.

Contribution

It proposes a novel $k$-essence scenario for EDE where the transition timing is linked to cosmic epochs, and analyzes its feasibility and limitations.

Findings

$k$-essence cannot fully realize the proposed EDE scenario.

A different $k$-essence model can trigger EDE ending at radiation-matter transition.

The model partially addresses the coincidence problem.

Abstract

Early dark energy (EDE) that becomes subdominant around the epoch of matter-radiation equality can be used to ease the Hubble tension. However, there is a theoretical problem that why the energy scale of EDE is in coincidence with that of matter-radiation equality when their physics are completely unrelated. Sakstein and Trodden [Phys. Rev. Lett. 124, 161301 (2020)] proposed a mechanism to solve this coincidence problem with $\mathcal{O}({\rm eV})$-mass neutrino. In this paper, in order to solve the coincidence problem, we propose a new scenario for EDE, in which the onset and ending of EDE are triggered by the radiation-matter transition. The specific example we study is a $k$-essence model. The cosmic evolution equations can be recast into a two-dimensional dynamical system and its main properties are analyzed. Our results suggest that $k$-essence seems unable to realize the new scenario for EDE. However, an EDE model with different scenario is realized in $k$-essence. In this model, the ending of EDE can be triggered by the radiation-matter transition while the onset depends on the initial conditions of the scalar field. Therefore, the obtained model can only be used to solve half of the coincidence problem. The full resolution in the framework of our initial proposed scenario is worthy of more research.