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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(R); 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(R) and f(T) gravities, we have considered some particular forms of f(R) 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.