K-chameleon and the coincidence problem

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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 $\mathbf{K}$ attractor and the other is a completely new, dubbed $\mathbf{C}$ attractor. Once the Universe is attracted into the $\mathbf{C}$ attractor, the fraction energy densities of the $k$-chameleon ${\ensuremath{\Omega}}_{\ensuremath{\phi}}$ and dust matter ${\ensuremath{\Omega}}_{m}$ are fixed and comparable, and the Universe will undergo a power-law accelerated expansion. One can adjust the model so that the $\mathbf{K}$ attractor does not appear. Thus, the $k$-chameleon model provides a natural solution to the cosmological coincidence problem.