Cosmographic Footprints of Dynamical Dark Energy

Abstract

We introduce a novel cosmographic framework to trace the late-time kinematics of the Universe without assuming any underlying dynamics. The method relies on generalized Padé-$(2,1)$ expansions around arbitrary pivot redshifts, which, compared to state-of-the-art calculations, reduce truncation errors by up to two orders of magnitude at high redshift and yield more precise constraints by defining cosmographic parameters exactly where the data lie. This avoids extrapolations, mitigates degeneracies, and enables a clean disentangling of their effects. Using the latest low-redshift datasets, we center the generalized expansion in multiple bins across $z\in[0,1]$ and obtain precise constraints on the redshift evolution of cosmographic parameters. We find that all key parameters deviate from their $Λ$CDM predictions in a redshift-dependent way that can be naturally explained within dynamical Dark Energy scenarios. The deceleration parameter $q(z)$ follows a redshift evolution consistent with the Chevallier-Polarski-Linder (CPL) parameterization, while the generalized $Om(z)$ diagnostic shows deviations of up to $\sim4σ$ from the constant $Λ$CDM expectation, closely matching the CPL predictions. Taken together, these results point to footprints of dynamical Dark Energy in the kinematics of the Universe at $z\lesssim 1$.

Figures (7)

• Figure 1: Cosmographic constraints on the deceleration parameter $q(z)$ at different redshift bins with 68% CL uncertainties (red points). The blue band shows the $\Lambda$CDM predictions, while the green band corresponds to those from a CPL model of dynamical DE, referred to as $w_0w_a$CDM. The left panel shows results obtained by combining Planck (or Planck $r_d$), DESI, and CC with PP SNIa. The right panel shows results from the same data combination but with DESy5 instead of PP. The bottom panels display the distance of the cosmographic points from the model predictions in units of the combined uncertainty $\Delta\sigma$. Blue circles correspond to $\Lambda$CDM and green crosses to $w_0w_a$CDM, providing a direct measure of the level of agreement between the cosmographic constraints and those derived within the respective cosmological models.
• Figure 2: 2D correlations between the constraints on the expansion rate, the deceleration parameter, and the jerk parameter obtained at 11 different pivot redshifts, from $z_0=0$ (far left) to $z_0=1$ (far right).
• Figure 3: Cosmographic constraints on the $Om(z)$ diagnostic at different redshift bins with 68% CL uncertainties (red points). The blue band shows the $\Lambda$CDM predictions ($Om(z)=\Omega_m$), while the green band corresponds to those from a CPL model of dynamical DE, referred to as $w_0w_a$CDM. The left panel shows results obtained by combining Planck (or Planck $r_d$), DESI, and CC with PP SNIa. The right panel shows results from the same data combination but with DESy5 instead of PP. The bottom panels display the distance of the cosmographic points from the model predictions in units of the combined uncertainty $\Delta\sigma$. Blue circles correspond to $\Lambda$CDM and green crosses to $w_0w_a$CDM, providing a direct measure of the level of agreement between the cosmographic constraints and those derived within the respective cosmological models.
• Figure 4: Comparison of the relative precision of the Padé expansion for $H(z)$ and $D_{\rm L}(z)$ at different redshifts $z$ (using exact $\Lambda$CDM predictions computed with CLASS as reference) for four representative choices of the pivot redshift $z_0$. The black dashed line shows the Padé expansion around $z_0=0$, corresponding to the standard case commonly discussed in the literature.
• Figure 5: Whisker plot summarizing the 68% CL constraints on the cosmographic parameters $H(z_0)$, $q(z_0)$, $j(z_0)$, and $s(z_0)$ at different pivot redshifts $z_0\in[0,1]$, for all dataset combinations considered in this work. For clarity, the constraints are slightly displaced horizontally around each pivot.