N. Nazari Pooya

In this study, we investigate two widely recognized interacting dark energy (IDE) models and assess their compatibility with observational data, focusing on the growth rate of matter perturbations. We explore IDE models with different equation of state (EOS) parameters for dark energy (DE), including the Chevallier-Polarski-Linder parametrization and a constant value for $w_{\mathrm{de}}$. To constrain the parameters of the IDE models using background data, we employ a Markov chain Monte Carlo (MCMC) analysis. Our results show that both IDE-I and IDE-II models are compatible with observational data, although with slight variations influenced by the homogeneity or clustering of DE. Following that, we investigate the growth of matter perturbations and perform a comprehensive statistical analysis utilizing both the background and growth rate data. The growth rate in IDE models exhibits deviations compared to the $\mathrm{\Lambda }\mathrm{CDM}$ model due to the impact of homogeneity or clustering of DE, as well as the selection of the EOS parameter. However, we find that the IDE models show good compatibility with the growth rate data. Furthermore, we explore how the clustering or homogeneity of DE and the selection of the EOS parameter affect the evolution of the relative difference in the growth rate of IDE models, $\mathrm{\Delta }f$, in comparison to the $\mathrm{\Lambda }\mathrm{CDM}$ model. Lastly, we employ the Akaike and Bayesian information criteria to evaluate and identify the best model that is compatible with the observational data. The selection of the model depends on the homogeneity or clustering of DE, the EOS parameter, and the dataset used. Overall, the IDE-I and IDE-II models exhibit agreement with the data, with slight deviations depending on specific scenarios and parameters.

In this work, we investigate the growth of matter perturbations in some known parameterizations of dark energy (DE) models i.e, CPL, JBP, BA, and a new parameterization of DE introduced in this study. We examine the growth of perturbations in the linear region by assuming the possibility of perturbations in DE. Then, we follow an overall likelihood analysis to put the same constraints on models using background and growth rate data, and we conclude that the reviewed DE parameterizations are compatible with the observational data at both background and perturbation levels. Furthermore, we find that DE parameterizations are comparable with each other, and with the $$ \Lambda $$Λ CDM model. In particular, we obtain the following significant results: (i) the growth rate of matter perturbations in the homogeneous DE case is smaller than its value in the clustered case for CPL and BA models, while it is the opposite for JBP and the new model. (ii) The growth rate of matter perturbations related to the CPL and BA models have very similar behavior for both homogeneous and clustered DE cases at all redshift z. This is also true for JBP and the new model. (iii) We show that the growth rate of matter perturbations relevant to the models is lower than its value in the $$\Lambda $$Λ CDM model at low redshifts, and at high redshifts, the difference between them is insignificant. Finally, using AIC and BIC analysis, we conclude that the selection of a model that has better compatible with the observational data depends on the background and perturbation data.

The generalized Chaplygin gas (GCG) model in spatially flat universe is investigated. The cosmological consequences led by GCG model including the evolution of EoS parameter, deceleration parameter and dimensionless Hubble parameter are calculated. We show that the GCG model behaves as a general quintessence model. The GCG model can also represent the pressureless CDM model at the early time and cosmological constant model at the late time. The dependency of transition from decelerated expansion to accelerated expansion on the parameters of model is investigated. The statefinder parameters $r$ and $s$ in this model are derived and the evolutionary trajectories in $s-r$ plane are plotted. Finally, based on current observational data, we plot the evolutionary trajectories in $s-r$ and $q-r$ planes for best fit values of the parameters of GCG model. It has been shown that although, there are similarities between GCG model and other forms of chaplygin gas in statefinder plane, but the distance of this model from the $\Lambda$CDM fixed point in $s-r$ diagram is shorter compare with standard chaplygin gas model.

In this paper, the holographic dark energy model with new infrared cut-off proposed by Granda and Oliveros has been investigated in spatially non flat universe. The dependency of the evolution of equation of state, deceleration parameter and cosmological evolution of Hubble parameter on the parameters of new HDE model are calculated. Also, the statefinder parameters $r$ and $s$ in this model are derived and the evolutionary trajectories in $s-r$ plane are plotted. We show that the evolutionary trajectories are dependent on the model parameters of new HDE model. Eventually, in the light of SNe+BAO+OHD+CMB observational data, we plot the evolutionary trajectories in $s-r$ and $q-r$ planes for best fit values of the parameters of new HDE model.