Dilaton Dark Energy Model in f(R), f(T) and Horava-Lifshitz Gravities

In this work, we have considered dilaton dark energy model in Weyl-scaled induced gravitational theory in presence of barotropic fluid. It is to be noted that the dilaton field behaves as a quintessence. Here we have discussed the role of dilaton dark energy in modified gravity theories namely, f®; f(T) and Horava-Lifshitz gravities and analyzed the behaviour of the dilaton field and the corresponding potential in respect to these modified gravity theories instead of Einstein’s gravity. In f® and f(T) gravities, we have considered some particular forms of f® and f(T) and we have shown that the potentials always increase with the dilaton fields. But in Horava-Lifshitz gravity, it has been seen that the potential always decreases as dilation field increases.