TDCOSMO. IX. Systematic comparison between lens modelling software
  programs: time delay prediction for WGD 2038$-$4008
  The importance of alternative methods to measure the Hubble constant such as
time-delay cosmography is highlighted by the recent Hubble tension. It is
paramount to thoroughly investigate and rule out systematic biases in all
measurement methods before we can accept new physics as the source of this
tension. In this study, we perform a check for systematic biases in the lens
modelling procedure of time-delay cosmography by comparing independent and
blind time-delay predictions of the system WGD 2038$-$4008 from two teams using
two different software programs: Glee and lenstronomy. The predicted time
delays from both teams incorporate the stellar kinematics of the deflector and
the external convergence from line-of-sight structures. The unblinded
time-delay predictions from the two teams agree within $1.2\sigma$ implying
that once the time delay is measured the inferred Hubble constant will also be
mutually consistent. However, there is a $\sim$4$\sigma$ discrepancy between
the power-law model slope and external shear, which is a significant
discrepancy at the level of lens models before incorporating the stellar
kinematics and the external convergence. We identify the difference in the
reconstructed point spread function (PSF) to be the source of this discrepancy.
If the same reconstructed PSF is used by both teams, then we achieve excellent
agreement within $\sim$0.6$\sigma$, indicating that potential systematics
stemming from source reconstruction algorithms and investigator choices are
well under control. We recommend future studies to supersample the PSF as
needed and marginalize over multiple algorithms/realizations for the PSF
reconstruction to mitigate the systematic associated with the PSF. A future
study will measure the time delays of the system WGD 2038$-$4008 and infer the
Hubble constant based on our mass models.
