Constraints to Dark Energy Using PADE Parameterizations

We put constraints on dark energy (DE) properties using PADE parameterization, and compare it to the same constraints using Chevalier-Polarski-Linder (CPL) and ACDM, at both the background and the perturbation levels. The DE equation of the state parameter of the models is derived following the mathematical treatment of PADE expansion. Unlike CPL parameterization, PADE approximation provides different forms of the equation of state parameter that avoid the divergence in the far future. Initially we perform a likelihood analysis in order to put constraints on the model parameters using solely background expansion data, and we find that all parameterizations are consistent with each other. Then, combining the expansion and the growth rate data, we test the viability of PADE parameterizations and compare them with CPL and ACDM models, respectively. Specifically, we find that the growth rate of the current PADE parameterizations is lower than ACDM model at low redshifts, while the differences among the models are negligible at high redshifts. In this context, we provide for the first time a growth index of linear matter perturbations in PADE cosmologies. Considering that DE is homogeneous, we recover the well-known asymptotic value of the growth index (namely γ = 3(W-1)/6W-5), while in the case of clustered DE, we obtain γ ≃ 3W (3W-5)/ (6W-5) (3W-1) . Finally, we generalize the growth index analysis in the case where γ is allowed to vary with redshift, and we find that the form of g (z) in PADE parameterization extends that of the CPL and ACDMcosmologies, respectively.