K-chameleon and the coincidence problem

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