Intrinsic Degeneracy of Gravitational Lens Time Delays: the case for a simple quadruple system in ΛCDM 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 ($\Omega, \Lambda$) to the standard values of $\Lambda$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 $\Lambda$ from strong lenses even more daunting.