Impact of Large-Scale Structure along Line-of-Sight on Time-Delay Cosmography

Time-delay cosmography, by monitoring the multiply imaged gravitational lenses in the time domain, offers a promising and independent method for measuring cosmological distances. However, in addition to the main deflector that produces the multiple images, the large-scale structure along the line-of-sight (LoS) will also deflect the traveling light rays, known as weak lensing (WL). Due to resolution limitations, accurately measuring WL on arcsecond scales is highly challenging. In this work, we evaluate the LoS effects on both lensing images and time-delay measurements using a more straightforward, high-resolution N-body simulation that provides a more realistic matter distribution compared to the traditional, computationally cheaper halo rendering method. We employ the multi-plane ray tracing technique, which is traditionally utilized to compute WL effects at the arcminute scale, extending its application to the strong lensing regime at the arcsecond scale. We focus on the quadruple-image system and present the following findings: 1. In addition to a constant external convergence, large-scale structures within a region approximately 2 arcminutes in angular size act as external perturbers, inducing inhomogeneous fluctuations on the arcsecond scale; 2. These fluctuations cannot be fully accounted for by external shear alone, necessitating the inclusion of external flexion; 3. While incorporating flexion provides a reasonably good fit to the lensing image, the time-delay distance still exhibits a $6.2$\textperthousand~bias and a $2.5\%$ uncertainty. This underscores the limitations of the single-plane approximation, as time-delay errors accumulate along the LoS.