The cosmological lens equation and the equivalent singleplane gravitational lens
Abstract
The gravitational lens equation resulting from a single (nonlinear) mass concentration (the main lens) plus inhomogeneities of the largescale structure is shown to be strictly equivalent to the singleplane gravitational lens equation without the cosmological perturbations. The deflection potential (and, by applying the Poisson equation, also the mass distribution) of the equivalent singleplane lens is derived. If the main lens is described by elliptical isopotential curves plus a shear term, the equivalent singleplane lens will be of the same form. Owing to the equivalence shown, the determination of the Hubble constant from time delay measurements is affected by the same masssheet invariance transformation as for the singleplane lens. If the lens strength is fixed (e.g. by measuring the velocity dispersion of stars in the main lens), the determination of H_0 is affected by inhomogeneous matter between us and the lens. The orientation of the mass distribution relative to the image positions is the same for the cosmological lens situation and the singleplane case. In particular this implies that cosmic shear cannot account for a misalignment of the observed galaxy orientation relative to the bestfitting lens model.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 December 1997
 DOI:
 10.1093/mnras/292.3.673
 arXiv:
 arXiv:astroph/9706185
 Bibcode:
 1997MNRAS.292..673S
 Keywords:

 Gravitational Lenses;
 Dark Matter;
 Mass Distribution;
 Hubble Constant;
 Computational Astrophysics;
 Poisson Equation;
 Equivalence;
 Time Lag;
 Transformations (Mathematics);
 Cosmology;
 Astrophysics;
 GRAVITATION;
 DARK MATTER;
 GRAVITATIONAL LENSING;
 LARGESCALE STRUCTURE OF UNIVERSE;
 Astrophysics
 EPrint:
 TeX, 11 pages, submitted to MNRAS