Systematic errors on optical-SED stellar mass estimates for galaxies
  across cosmic time and their impact on cosmology
  Studying galaxies at different cosmic epochs entails several observational
effects that need to be taken into account to compare populations across a
large time span in a consistent manner. We use a sample of 166 nearby galaxies
that hosted type Ia supernovae (SNe Ia) and have been observed with the
integral field spectrograph MUSE through the AMUSING survey. Here, we present a
study of the systematic errors and bias in the host stellar mass with
increasing redshifts that are generally overlooked in SNe Ia cosmological
analyses. We simulate observations at different redshifts (0.1<z<2.0) using
four photometric bands (griz, similar to the Dark Energy Survey-SN program) to
then estimate the host galaxy properties across cosmic time. We find that
stellar masses are systematically underestimated as we move towards higher
redshifts, due mostly to different rest-frame wavelength coverage, with
differences reaching 0.3 dex at z~1. We have used the newly derived corrections
as a function of redshift to correct the stellar masses of a known sample of SN
Ia hosts and derive cosmological parameters. We show that these corrections
have a small impact on the derived cosmological parameters. The most affected
is the value of the mass step $\Delta_M$, which is reduced by $\sim$0.004 (6%
lower). The dark energy equation of state parameter $w$ changes by $\Delta w
\sim $0.006 (0.6% higher) and the value of $\Omega_m$ increases at most by
0.001 ($\sim$0.3%), all within the derived uncertainties of the model. While
the systematic error found in the estimate of the host stellar mass does not
significantly affect the derived cosmological parameters, it is an important
source of a systematic error that one should correct for as we enter a new era
of precision cosmology.
