We investigate the holographic, new agegraphic and ghost dark energy models in the framework of fractal cosmology. We consider a fractal FRW universe filled with the dark energy and dark matter. We obtain the equation of state parameters of the selected dark energy models in the ultraviolet regime and discuss on their implications. Keywords: Dark energy; Fractal cosmology Fractal cosmologyRecently, Calcagni [1, 2] gave a quantum gravity in a fractal universe and then investigated cosmology in that framework. That theory is Lorentz invariant, power-counting renormalizable and free from ultraviolet divergence. In the present paper, we study few DE models (including holographic, new agegraphic and ghost DE) in the framework of fractal cosmology proposed by Calcagni. We calculate their equation of state parameters and discuss their physical implications via graphs and conclude in the end.The action of Einstein gravity in a fractal spacetime is given by [1, 2]where κ 2 = 8πG. Also G, g, R, Λ and L m are the gravitational constant, determinant of metric g µν , Ricci scalar, cosmological constant and Lagrangian density of the total matter inside the universe, respectively. The quantities v and ω are the fractal function and fractal parameter, respectively. Note that d̺(x) is Lebesgue-Stieltjes measure generalizing the standard 4-dimensional measure d 4 x. The scaling dimension of ̺ is [̺] = −4α, where α > 0 is a parameter. The values of α in the infrared (IR) and ultraviolet (UV) regimes are α IR = 1 and α UV = 1/2,

We study the correspondence between the interacting viscous ghost dark energy model with the tachyon, K-essence and dilaton scalar field models in the framework of Einstein gravity. We consider a spatially non-flat FRW universe filled with interacting viscous ghost dark energy and dark matter. We reconstruct both the dynamics and potential of these scalar field models according to the evolutionary behavior of the interacting viscous ghost dark energy model, which can describe the accelerated expansion of the universe. Our numerical results show that the interaction and viscosity have opposite effects on the evolutionary properties of the ghost scalar filed models.PACS numbers: 98.80.−k, 95.36.+x

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Within the framework of DBI non-canonical scalar field model of dark energy, we study the growth of dark matter perturbations in both the linear and non-linear regimes. In our DBI model, we consider the anti-de Sitter warp factor f (φ) = f 0 φ −4 with constant f 0 > 0 and assume the DBI dark energy to be clustered and its sound speed c s to be constant. In the linear regime, we use the Pseudo-Newtonian formalism to obtain the growth factor of dark matter perturbations and conclude that for smaller, the growth factor of dark matter is smaller for clustering DBI model compared to the homogeneous one. In the non-linear regime based on the spherical collapse model, we obtain the linear overdensity δ c (z c ), the virial overdensity ∆ vir (z c ), overdensity at the turn around ζ(z c ) and the rate of expansion of collapsed region h ta (z). We point out that for the smaller c s (orf 0 ), the values of δ c (z c ), ∆ vir (z c ), ζ(z c ) and h ta (z) in non-clustering DBI models deviate more than the ΛCDM compared to the clustering DBI models. Finally, with the help of spherical collapse parameters we calculate the relative number density of halo objects above a given mass and conclude that the differences between clustering and homogeneous DBI models are more pronounced for the higher-mass halos at high redshift.