In this work, we have considered a model of the flat Friedmann-Robertson-Walker (FRW) Universe filled with cold dark matter and a chameleon field where the scale function is taken as (i) intermediate expansion and (ii) logamediate expansion. In both cases we find the expressions of the chameleon field, chameleon potential, statefinder parameters, and slow-roll parameters. Also, it has been shown that the potential always decreases with the chameleon field in both scenarios. The nature of the slow-roll parameters has been shown diagrammatically.

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 Hořava-Lifshitz gravities and analyzed the behavior 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 Hořava-Lifshitz gravity, it has been seen that the potential always decreases as dilation field increases.

In this work, we have considered Cardassian Universe in Hořava-Lifshitz gravity. Four types of Cardassian Universe models i.e., polytropic/power law, modified polytropic, exponential and modified exponential models have been considered for accelerating models. The natures of statefinder parameters, deceleration parameter, Om diagnostic and EoS parameters have been investigated for all types of Cardassian models in Hořava-Lifshitz gravity.

We have considered a model of two component mixture i.e., mixture of Chaplygin gas and barotropic fluid with tachyonic field. In the case, when they have no interaction then both of them retain their own properties. Let us consider an energy flow between barotropic and tachyonic fluids. In both the cases we find the exact solutions for the tachyonic field and the tachyonic potential and show that the tachyonic potential follows the asymptotic behavior. We have considered an interaction between these two fluids by introducing a coupling term. Finally, we have considered a model of three component mixture i.e., mixture of tachyonic field, Chaplygin gas and barotropic fluid with or without interaction. The coupling functions decays with time indicating a strong energy flow at the initial period and weak stable interaction at later stage. To keep the observational support of recent acceleration we have considered two particular forms (i) Logamediate Scenario and (ii) Intermediate Scenario, of evolution of the Universe. We have examined the natures of the recent developed statefinder parameters and slow-roll parameters in both scenarios with and without interactions in whole evolution of the universe.

We have considered the generalized holographic and generalized Ricci dark energy models for acceleration of the universe. If the universe filled with only GHDE/GRDE the corresponding deceleration parameter, EOS parameter and statefinder parameters have been calculated. Next we have considered that the mixture of GHDE/GRDE and dark matter in interacting and non-interacting situations. Also the mixture of GHDE/GRDE and generalized Chaplygin gas have been analyzed during evolution of the universe. The natures of above mentioned parameters have been investigated for interacting and non-interacting situations. Finally, it follows that the prescribed models derive the acceleration of the universe.