From Hubble to Snap Parameters: A Gaussian Process Reconstruction

By using recent $H(z)$ and SNe Ia data, we reconstruct the evolution of kinematic parameters $H(z)$, $q(z)$, jerk and snap, using a model-independent, non-parametric method, namely, the Gaussian Processes. Throughout the present analysis, we have allowed for a spatial curvature prior, based on Planck 18 [1] constraints. In the case of SNe Ia, we modify a python package (GaPP) [2] in order to obtain the reconstruction of the fourth derivative of a function, thereby allowing us to obtain the snap from comoving distances. Furthermore, using a method of importance sampling, we combine $H(z)$ and SNe Ia reconstructions in order to find joint constraints for the kinematic parameters. We find for the current values of the parameters: $H_0=67.2\pm 6.2$ km/s/Mpc, $q_0=-0.60_{-0.18}^{+0.21}$, $j_0=0.90_{-0.65}^{+0.75}$, $s_0=-0.57_{-0.31}^{+0.52}$ at 1$\sigma$ c.l. We find that these reconstructions are compatible with the predictions from flat $\mathrm{\Lambda }$CDM model, at least for 2$\sigma$ confidence intervals.