Gravitational lenses and the inhomogeneous universe

Abstract

The theory of static gravitatonal lenses is discussed using the optical scalar formalism and the ray-bending approximation to this formalism. The advantages of each approach are discussed, with particular emphasis on the use of the bending approximation for discretely observable lenses, say multiply imaged quasars, and the optical scalar equations for cumulative effects of inhomogeneities for distant objects in the universe.The effect of a locally lumpy distribution on the past null cone of a typical observer is discussed. This is of particular interest in deciding the limits to which one can hope to do cosmology through the use of optical and other telescopes. The optical-scalar-equation driving terms can be replaced by appropriately defined mean driving terms for subsets of observable objects, and coupled with corresponding probabilities, these calculations can yield estimates of the "thickness" of the observer's past null cone as a function of the red shift. This imposes a limit on the use of standard observations in determining the structure of the universe, simply owing to the "fuzzy" structure of the perceived past null cone.