K-Chameleon and the Coincidence Problem

TL;DR

This paper introduces a hybrid k-chameleon model combining k-essence and chameleon mechanisms, which naturally explains the cosmological coincidence problem through specific attractor solutions during matter domination.

Contribution

The paper proposes a novel hybrid k-chameleon model with unique attractors that address the coincidence problem, extending previous k-essence and chameleon theories.

Findings

Identifies two attractors: K and C, with C leading to accelerated expansion.

C attractor fixes energy density fractions of dark energy and matter.

Model can be tuned to exclude the K attractor, solving the coincidence problem.

Abstract

In this paper we present a hybrid model of k-essence and chameleon, named as k-chameleon. In this model, due to the chameleon mechanism, the directly strong coupling between the k-chameleon field and matters (cold dark matters and baryons) is allowed. In the radiation dominated epoch, the interaction between the k-chameleon field and background matters can be neglected, the behavior of the k-chameleon therefore is the same as that of the ordinary k-essence. After the onset of matter domination, the strong coupling between the k-chameleon and matters dramatically changes the result of the ordinary k-essence. We find that during the matter-dominated epoch, only two kinds of attractors may exist: one is the familiar {\bf K} attractor and the other is a completely {\em new}, dubbed {\bf C} attractor. Once the universe is attracted into the {\bf C} attractor, the fraction energy densities of the k-chameleon $\Omega_{\phi}$ and dust matter $\Omega_m$ are fixed and comparable, and the universe will undergo a power-law accelerated expansion. One can adjust the model so that the {\bf K} attractor do not appear. Thus, the k-chameleon model provides a natural solution to the cosmological coincidence problem.