Over-constrained Gravitational Lens Models and the Hubble Constant

TL;DR

This paper demonstrates that over-constrained gravitational lens models can produce precise but inaccurate estimates of the Hubble constant, suggesting current measurements may not be as accurate as claimed.

Contribution

It reveals the limitations of simple lens models in accurately estimating the Hubble constant and highlights the potential for overconfidence in current measurements.

Findings

Simple lens models can produce precise but biased H0 estimates.

Current H0 estimates from lensing are unlikely to be more accurate than 10%.

Over-constrained models lead to inaccurate H0 despite high precision.

Abstract

It is well known that measurements of H0 from gravitational lens time delays scale as H0~1-k_E where k_E is the mean convergence at the Einstein radius R_E but that all available lens data other than the delays provide no direct constraints on k_E. The properties of the radial mass distribution constrained by lens data are R_E and the dimensionless quantity x=R_E a''(R_E)/(1-k_E)$ where a''(R_E) is the second derivative of the deflection profile at R_E. Lens models with too few degrees of freedom, like power law models with densities ~r^(-n), have a one-to-one correspondence between x and k_E (for a power law model, x=2(n-2) and k_E=(3-n)/2=(2-x)/4). This means that highly constrained lens models with few parameters quickly lead to very precise but inaccurate estimates of k_E and hence H0. Based on experiments with a broad range of plausible dark matter halo models, it is unlikely that any current estimates of H0 from gravitational lens time delays are more accurate than ~10%, regardless of the reported precision.