TDCOSMO. IX. Systematic comparison between lens modelling software programs: time delay prediction for WGD 2038-4008

The importance of alternative methods for measuring 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 the two teams incorporate the stellar kinematics of the deflector
and the external convergence from line-of-sight structures. The un-blinded
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 the stellar kinematics and the
external convergence are incorporated. We identify the difference in the
reconstructed point spread function (PSF) to be the source of this discrepancy.
When the same reconstructed PSF was used by both teams, we achieved 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 that future studies supersample the PSF as
needed and marginalize over multiple algorithms or realizations for the PSF
reconstruction to mitigate the systematics 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.