New parameterizations of generalized Chaplygin gas model constrained at background and perturbation levels

Abstract: We study the main cosmological properties of the Generalized Chaplygin Gas (GCG) dark energy model at the background and perturbation levels. By using the latest cosmological data in both the background and perturbation levels, we implement a joint likelihood analysis to constrain the cosmological parameters of the model. Using the available expansion and growth rate data, we place constraints on the free parameters of the GCG model based on the statistical Markov chain Monte Carlo method. Then, the best-fit values of cosmological parameters and those of confidence regions are found. We obtain the best-fit value of the current expansion rate of the universe in the GCG model and show that it is in good agreement with the $\Lambda$CDM model. Moreover, the growth rate of matter perturbations is investigated in the context of a unified GCG model. It is shown that in this model, the dark energy component, like the $\Lambda$ sector in the $\Lambda$CDM model, can suppress the amplitude of matter perturbations. We show that the growth rate of perturbations in GCG parametrization is consistent with cluster-scale observations similar to the case of the concordance $\Lambda$CDM model. Our results show that the tension on $\sigma_{8}$ appeared in concordance model can be alleviated in GCG cosmology.