There are two possible causes of variability in gravitationally lensed quasars: intrinsic fluctuations of the quasar and “microlensing ” by compact objects along the line of sight. If disentangled from each other, microlens-induced variability can be used to study two cosmological issues of great interest, the size and brightness profile of quasars on one hand, and the distribution of compact (dark) matter along the line of sight. Here we present a summary of recent observational evidence for quasar microlensing as well as of theoretical progress in the field. Particular emphasis is given to the questions which microlensing can address regarding the search for dark matter, both in the halos of lensing galaxies and in a cosmologically distributed form. A discussion of desired observations and required theoretical studies is presented as a conclusion/outlook. 1 What is Microlensing of Quasars? 1.1 Mass, length and time scales The lensing effects on quasars by compact objects in the mass range 10−6 ≤ m/M ⊙ ≤ 103 is usually called “quasar microlensing”. The microlenses can be ordinary stars, brown dwarfs, planets, black holes, molecular clouds, globular clusters or other compact mass concentrations (as long as their physical size is smaller than their Einstein radius). In most practical cases, the microlenses are part of a galaxy which acts as the main (macro-)lens. However, microlenses could also be located in, say, clusters of galaxies or they could even be imagined “free floating” and filling intergalactic space. The relevant length scale for microlensing (in the quasar plane) is the Einstein radius of the lens: rE
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