Impact of Large-scale Structure along the Line of Sight on Time-delay Cosmography

Abstract

Time-delay cosmography offers a promising and independent method for measuring cosmological distances by monitoring multiple images of gravitationally lensed sources. However, beyond the main deflector, large-scale structure along the line of sight (LoS) also deflects travelling light rays via weak lensing (WL). Due to resolution limitations, accurately measuring WL on arcsecond scales remains 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 multiplane 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 quadruple-image systems and present the following findings: (1) In addition to a constant external convergence, large-scale structures within a region approximately 2′ in angular size act as external perturbers, inducing inhomogeneous fluctuations on the arcsecond scale. (2) Standard single-plane models suffer from severe geometric degeneracies between foreground shear and main lens ellipticity. By ignoring complex multiplane couplings, these models fail to accurately recover the external convergence, producing broad, bimodal errors. (3) Explicitly accounting for the LoS shear via the minimal lens model successfully breaks these degeneracies, yielding robust and tightly constrained reconstructions. (4) Uncorrected foreground convergence introduces a 0.5%∼0.7% systematic bias in time-delay distance estimation. Our findings highlight that advanced LoS modeling is indispensable for precision time-delay cosmography.