Comments on the mass sheet degeneracy in cosmography analyses

  Luca Teodori [1]  ,  Kfir Blum [1]  ,  Emanuele Castorina [2]  ,  Marko Simonovic [3]  ,  Yotam Soreq [4]  
[1] Weizmann Institute, Department of Particle Physics and Astrophysics
[2] Dipartimento di Fisica ‘Aldo Pontremoli’, Universita’ degli Studi di Milano
[3] Theoretical Physics Department, CERN, 1 Esplanade des Particules
[4] Physics Department, Technion

We make a number of comments regarding modeling degeneracies in strong lensing measurements of the Hubble parameter H_0. The first point concerns the impact of weak lensing associated with different segments of the line of sight. We show that external convergence terms associated with the lens-source and observer-lens segments need to be included in cosmographic modeling, in addition to the usual observer-source term, to avoid systematic bias in the inferred value of H_0. Specifically, we show how an incomplete account of some line of sight terms biases stellar kinematics as well as ray tracing simulation methods to alleviate the mass sheet degeneracy. The second point concerns the use of imaging data for multiple strongly-lensed sources in a given system. We show that the mass sheet degeneracy is not fully resolved by the availability of multiple sources: some degeneracy remains because of differential external convergence between the different sources. Similarly, differential external convergence also complicates the use of multiple sources in addressing the approximate mass sheet degeneracy associated with a local ("internal") core component in lens galaxies. This internal-external degeneracy is amplified by the non-monotonicity of the angular diameter distance as a function of redshift. For a rough assessment of the weak lensing effects, we provide estimates of external convergence using the nonlinear matter power spectrum, paying attention to non-equal time correlators.