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Abstract
In the framework of fractal universe, the unified models of dark energy and dark matter are being presented with the background of homogenous and isotropic FLRW geometry. The aspects of fractal cosmology helps in better understanding of the universe in different dimensions. Relationship between the squared speed of the sound and the equation of state parameter is the key feature of these models. We have used constant as well as variable forms of speed of sound and express it as a function of equation of state parameter. By utilizing the four different forms of speed of sound, we construct the energy densities and pressures for these models and then various cosmological parameters like hubble parameter, EoS parameter, deceleration parameter and Om- diagnostic are investigated. Graphical analysis of these parameters show that in most of the cases EoS parameters and trajectories of Om-diagnostic corresponds to the quintessence like nature of the universe and the deceleration parameters represent accelerated and decelerated phase. In the end, we remark that cosmological analysis of these models indicates that these models correspond to different well known dark energy models.
Highlights
Many theoretical ideas have been suggested to explore the nature and origin of the dark energy, they include the cosmological constant, modified matter models, modified gravity models
We have studied FRLW universe that is the combination of dark matter and dark energy
In various theories of quantum gravity, universe is described as a dimensional flow which has become a motivation for the fractal cosmology
Summary
Many theoretical ideas have been suggested to explore the nature and origin of the dark energy, they include the cosmological constant, modified matter models, modified gravity models. Calcogni [17,18] studied quantum gravity in the framework of fractal universe, he formulated a power counting renormalizable field theory which exists in fractal space time and without ultraviolet divergence. In this scenario near the two topological dimensions, the renormalizability of perturbative quantum gravity theories draw attention to D = 2 + models which can improve the understanding of four dimensions D = 4 [19,20,21]. Lemets et al [25] presented the main aspects for the fractal cosmology models They discussed the model with the interaction of DE and DM.
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