In this paper we examine the cosmological consequences of fourth order Galileon gravity. We carry out detailed investigations of the underlying dynamics and demonstrate the stability of one de~Sitter phase. The stable de~Sitter phase contains a Galileon field $\pi${} which is an increasing function of time ($\pi${}\ifmmode \dot{}\else \textperiodcentered \fi{}>0). Using the required suppression of the fifth force, supernovae, Baryon acoustic oscillations, and CMB data, we constrain parameters of the model. We find that the $\pi${} matter coupling parameter $\beta${} is constrained to small numerical values such that $\beta${}<0.02. We also show that the parameters of the third and fourth order in the action (c3,c4) are not independent and with reasonable assumptions, we obtain constraints on them. We investigate the growth history of the model and find that the subhorizon approximation is not allowed for this model. We demonstrate strong scale dependence of linear perturbations in the fourth order Galileon gravity.

In this paper, we carry out a study of viable cosmological models in f(R)~gravity at the background level. We use observable parameters like $\Omega${} and $\gamma${} to form an autonomous system of equations and show that the models under consideration exhibit two different regimes in their time evolution, namely, a phantom phase followed by a quintessencelike behavior. We employ state finder parameters to emphasize a characteristic discriminative signature of these models.

The string inspired tachyon field can serve as a candidate of dark energy. Its equation of state parameter $w$ varies from 0 to $-1$. In the case of tachyon field potential $V(\varphi )\to 0$ slower (faster) than $1/{\varphi }^2$ at infinity, dark energy (dark matter) is a late time attractor. We investigate the tachyon dark energy models under the assumption that $w$ is close to $-1$. We find that all the models exhibit unique behavior around the present epoch which is exactly the same as that of the thawing quintessence.