SNe Ia are used to determine the distance-redshift relation and build the
Hubble diagram. Neglecting their host-galaxy peculiar velocities (PVs) may bias
the measurement of cosmological parameters. The smaller the redshift, the
larger the effect is. We use realistic simulations of SNe Ia observed by the
Zwicky Transient Facility (ZTF) to investigate the effect of different methods
to take into account PVs. We study the impact of neglecting galaxy PVs and
their correlations in an analysis of the SNe Ia Hubble diagram. We find that it
is necessary to use the PV full covariance matrix computed from the velocity
power spectrum to take into account the sample variance. Considering the
results we have obtained using simulations, we determine the PV systematic
effects in the context of the ZTF DR2 SNe Ia sample. We determine the PV impact
on the intercept of the Hubble diagram, $a_B$, which is directly linked to the
measurement of $H_0$. We show that not taking into account PVs and their
correlations results in a shift of the $H_0$ value of about
$1.0$km.s$^{-1}$.Mpc$^{-1}$ and a slight underestimation of the $H_0$ error
bar.
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Title
ZTF SN Ia DR2: Peculiar velocities impact on the Hubble diagram