  Type Ia supernova (SN Ia) cosmology relies on the estimation of lightcurve
parameters to derive precision distances that leads to the estimation of
cosmological parameters. The empirical SALT2 lightcurve modeling that relies on
only two parameters, a stretch x1, and a color c, has been used by the
community for almost two decades. In this paper we study the ability of the
SALT2 model to fit the nearly 3000 cosmology-grade SN Ia lightcurves from the
second release of the Zwicky Transient Facility (ZTF) cosmology science working
group. While the ZTF data was not used to train SALT2, the algorithm is
modeling the ZTF SN Ia optical lightcurves remarkably well, except for
lightcurve points prior to -10 d from maximum, where the training critically
lacks statistics. We find that the lightcurve fitting is robust against the
considered choice of phase-range, but we show the [-10; +40] d range to be
optimal in terms of statistics and accuracy. We do not detect any significant
features in the lightcurve fit residuals that could be connected to the host
environment. Potential systematic population differences related to the SN Ia
host properties might thus not be accountable for by the addition of extra
lightcurve parameters. However, a small but significant inconsistency between
residuals of blue- and red-SN Ia strongly suggests the existence of a
phase-dependent color term, with potential implications for the use of SNe Ia
in precision cosmology. We thus encourage modellers to explore this avenue and
we emphasize the importance that SN Ia cosmology must include a SALT2
retraining to accurately model the lightcurves and avoid biasing the derivation
of cosmological parameters.
