Gravitational lensing by cosmic strings

We discuss the possible role of a cosmological distribution of vacuum strings in the gravitational imaging of quasars. Lensing properties are described for open strings and for large and small closed loops. A simplified model shows that small loops typically produce a pair of magnified merging images. This effect introduces an observational ‘amplification bias’ which causes magnified quasars to appear frequently in a flux-limited sample even though they are intrinsically rare. Highly magnified merging images are sensitive to small changes in the lens, and it is shown that loop oscillations can lead to observable variations in image size, configuration, and total luminosity. Furthermore, the functional form of this variability can be derived on the basis of universal properties of Lagrangian mappings near singularities. For example, the magnification varies as $$m \propto |t - t_\infty|^{-1/2}$$ where t_∞ is the time when the quasar crosses a caustic. At t_∞ the intensity becomes formally infinite, the two images merge and then suddenly vanish as the quasar passes to the other side of the caustic. The probability of observing lensing events with various properties are estimated in two simple scenarios, and the possibility of searching for them is discussed.