Cosmography with DESI DR2 and SN data

In this paper, we present a kinematic analysis of the Universe's expansion history using cosmography, with a particular emphasis on the jerk parameter ${j}_{0}$, which is equal to one in the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ scenario. We use distance measurements from DESI DR2, both independently and in combination with current type Ia supernova (SN) samples, to constrain the cosmographic parameters up to the fourth order without relying on a specific cosmological model. Our results show that, for the DESI DR2 data alone, the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ prediction (${j}_{0}=1$) falls within the $2\ensuremath{\sigma}$ confidence region. However, when DESI DR2 is combined with the Union3, $\mathrm{Pantheon}+$, and DESY5 SN datasets, the result obtained is discrepant with the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model at about $3.4\ensuremath{\sigma}$, $4.1\ensuremath{\sigma}$, and $5.4\ensuremath{\sigma}$, respectively. These results are consistent with the conclusions based on dark energy parametrizations reported by the DESI collaboration, which suggest the presence of a dynamic dark energy component in the Universe.