Dark energy reconstruction based on the Padé approximation; an expansion around the $$\varLambda $$ Λ CDM

Abstract We study the dynamical properties of dark energy based on a large family of Padé parameterizations for which the dark energy density evolves as the ratio between two polynomials in the scale factor of the universe. Using the latest cosmological data we perform a standard likelihood analysis in order to place constraints on the main cosmological parameters of different Padé models. We find that the basic cosmological parameters, namely $$({\varOmega _{m0}},h,{\sigma _{8}})$$ (Ωm0,h,σ8) are practically the same for all Padé parametrizations explored here. Concerning the free parameters which are related to dark energy we show that the best-fit values indicate that the equation of state parameter at the present time is in the phantom regime ($$w-1$$ w>-1 at $$1\sigma $$ 1σ level. Finally, for the current family of Padé parametrizations we test their ability, via AIC, BIC and Jeffreys’ scale, to deviate from $$\varLambda $$ Λ CDM cosmology. Among the current Padé parametrizations, the model which contains two dark energy parameters is the one for which a small but non-zero deviation from $$\varLambda $$ Λ CDM cosmology is slightly allowed by the AIC test. Moreover, based on Jeffreys’ scale we show that a deviation from $$\varLambda $$ Λ CDM cosmology is also allowed and thus the possibility of having a dynamical dark energy in the form of Padé parametrization cannot be excluded