Foreground biases in strong gravitational lensing

TL;DR

This paper investigates how ignoring foreground perturbers in strong gravitational lensing models introduces biases and uncertainties in measurements of cosmological parameters, especially the Hubble constant, due to degeneracies with lens properties.

Contribution

It derives the degeneracy between foreground shear and lens ellipticity, quantifies the bias in lens parameters, and assesses the impact on Hubble constant measurements.

Findings

Foreground shear degeneracy biases ellipticity measurements by a few percent.

Foreground convergence introduces about 1% uncertainty in H0.

Overdense lines of sight may cause a small overestimation of H0.

Abstract

Strong gravitational lensing is a competitive tool to probe the dark matter and energy content of the Universe. However, significant uncertainties can arise from the choice of lens model, and in particular the parameterisation of the line of sight. In this work, we consider the consequences of ignoring the contribution of foreground perturbers in lens modelling. We derive the explicit form of the degeneracy between the foreground shear and the ellipticity of a power law lens, which renders the former quantity effectively unmeasurable from strong lensing observables, and biases measurements of the latter by a few percent. Nonetheless, we demonstrate that this degeneracy does not affect measurements of the Einstein radius. Foreground tidal effects are also not expected to bias the slope of the potential, and any biases in this slope should not affect the recovery of the Hubble constant. The foreground convergence term adds an additional uncertainty to the measurement of $H_0$, and we show that this uncertainty will be on the order of $1\%$ for lensing systems located along random lines of sight. There is evidence to indicate that the probability of strong lensing is higher towards overdense lines of sight, and this could result in a small systematic bias towards overestimations of $H_0$.