Redshift dependence and dipolar velocity corrections in cosmographic reconstructions through Type Ia supernova samples

Abstract

We perform a cosmographic analysis of Type Ia supernovae using the Pantheon+\&SH0ES, DES-SNY5 and Union3 compilations. We consider different redshift intervals, analyzed through a third-order Taylor expansion and a Padé $(1,2)$ approximation of the luminosity distance. First, we first infer the cosmographic parameters directly from the observed supernova redshifts. Afterwards, we extend the analysis by including a dipole correction associated with the local peculiar velocity field, constraining both its amplitude and direction. For Pantheon+\&SH0ES, the Cepheid calibration allows a direct determination of the Hubble constant, whereas for DES-SNY5 and Union3 we fix $H_0$ to set the absolute distance scale. By progressively increasing the maximum redshift of the sample, we study how the inferred cosmographic parameters depend on the adopted redshift interval. We find that the Hubble constant obtained from Pantheon+\&SH0ES remains consistent with previous determinations for both cosmographic parameterizations. Instead, the agreement of the deceleration $q_0$ and jerk $j_0$ parameters with the $Λ$CDM values depends on the adopted compilation and improves mainly for Pantheon+\&SH0ES as the redshift interval is enlarged. Moreover, the reconstructed dipole parameters remain stable across the redshift intervals considered, with velocity amplitudes of order $300\,\mathrm{km\,s^{-1}}$, for all three supernova samples. Finally, fixing the dipole parameters with the cosmic microwave background values leads to a slight shift from the fiducial $Λ$CDM values of the deceleration $q_0$ and jerk $j_0$ parameters.