Mass-sheet degeneracy, power-law models and external convergence: Impact on the determination of the Hubble constant from gravitational lensing

TL;DR

This paper examines how the mass-sheet degeneracy and assumptions about lens galaxy mass profiles affect the accuracy of Hubble constant measurements from gravitational lensing, revealing significant potential biases.

Contribution

It demonstrates that common assumptions about power-law mass profiles can lead to substantial errors in H0 estimates, highlighting the need to reconsider degeneracy impacts.

Findings

Mass-sheet degeneracy introduces significant uncertainty in lensing-based H0 measurements.

Power-law models can be misleading, fitting data well but biasing H0 by about 20%.

Environmental effects do not fully break degeneracies in lens modeling.

Abstract

The light travel time differences in strong gravitational lensing systems allows an independent determination of the Hubble constant. This method has been successfully applied to several lens systems. The formally most precise measurements are, however, in tension with the recent determination of $H_0$ from the Planck satellite for a spatially flat six-parameters $\Lambda CDM$ cosmology. We reconsider the uncertainties of the method, concerning the mass profile of the lens galaxies, and show that the formal precision relies on the assumption that the mass profile is a perfect power law. Simple analytical arguments and numerical experiments reveal that mass-sheet like transformations yield significant freedom in choosing the mass profile, even when exquisite Einstein rings are observed. Furthermore, the characterization of the environment of the lens does not break that degeneracy which is not physically linked to extrinsic convergence. We present an illustrative example where the multiple imaging properties of a composite (baryons + dark matter) lens can be extremely well reproduced by a power-law model having the same velocity dispersion, but with predictions for the Hubble constant that deviate by $\sim 20%$. Hence we conclude that the impact of degeneracies between parametrized models have been underestimated in current $H_0$ measurements from lensing, and need to be carefully reconsidered.