Intrinsic Degeneracy of Gravitational Lens Time Delays: the case for a simple quadruple system in $\mathrm{\Lambda }$CDM cosmology

A degeneracy in strong lens model is shown analytically. The observed time delays and quasar image positions might {\it not} uniquely determine the concentration and the extent of the lens galaxy halo mass distribution. Simply hardwiring the Hubble constant ($H_0$) and the cosmology ($\mathrm{\Omega },\mathrm{\Lambda }$) to the standard values of $\mathrm{\Lambda }$CDM cosmology might {\it not} fully lift this degeneracy, which exists rigourously even with very accurate data. Equally good fits to the images could be found in lens mass models with either a mostly Keplerian or a flat rotation curve. This degeneracy in mass models makes the task of getting reliable $H_0$ and $\mathrm{\Lambda }$ from strong lenses even more daunting.