The influence of weak lensing on measurements of the Hubble constant with quad-image gravitational lenses

We investigate the influence of matter along the line of sight and in the strong lens vicinity on the properties of quad image configurations and on the measurements of the Hubble constant (H0). We use simulations of light propagation in a nonuniform universe model with the distribution of matter in space based on the data from Millennium Simulation. For a given strong lens and haloes in its environment we model the matter distribution along the line of sight many times, using different combinations of precomputed deflection maps representing subsequent layers of matter on the path of rays. We fit the simulated quad image configurations with time delays using nonsingular isothermal ellipsoids (NSIE) with external shear as lens models, treating the Hubble constant as a free parameter. We get a large artificial catalog of lenses with derived values of the Hubble constant, Hfit. The average and median of Hfit differ from the true value used in simulations by < 0.5 km/s/Mpc which includes the influence of matter along the line of sight and in the lens vicinity, and uncertainty in lens parameters, except the slope of the matter distribution, which is fixed. The characteristic uncertainty of Hfit is ~3 km/s/Mpc. Substituting the lens shear parameters with values estimated from the simulations reduces the uncertainty to ~2 km/s/Mpc.