The impact of line-of-sight structures on measuring $H_0$ with strong
  lensing time-delays
  Measurements of The Hubble-Lemaitre constant from early- and local-universe
observations show a significant discrepancy. In an attempt to understand the
origin of this mismatch, independent techniques to measure H0 are required. One
such technique, strong lensing time delays, is set to become a leading
contender amongst the myriad methods due to forthcoming large strong lens
samples. It is therefore critical to understand the systematic effects inherent
in this method. In this paper, we quantify the influence of additional
structures along the line-of-sight by adopting realistic light cones derived
from the CosmoDC2 semi-analytical extra-galactic catalogue. Using multiple lens
plane ray-tracing to create a set of simulated strong lensing systems, we have
investigated the impact of line-of-sight structures on time-delay measurements
and in turn, on the inferred value of H0. We have also tested the reliability
of existing procedures for correcting for line-of-sight effects. We find that
if the integrated contribution of the line-of-sight structures is close to a
uniform mass sheet, the bias in H0 can be adequately corrected by including a
constant external convergence $\kappa_{ext}$ in the lens model. However, for
realistic line-of-sight structures comprising many galaxies at different
redshifts, this simple correction overestimates the bias by an amount that
depends linearly on the median external convergence. We, therefore, conclude
that lens modelling must incorporate multiple lens planes to account for
line-of-sight structures for accurate and precise inference of H0.
