Cold Dark Matter and Strong Gravitational Lensing: Concord or Conflict?

(Abridged) Using the number and sizes of observed gravitational lenses, I derive upper limits on the dark matter content of elliptical galaxies. Galaxies built from Cold Dark Matter (CDM) mass distributions are too concentrated to comfortably satisfy these limits; SCDM is ruled out, and LCDM is only marginally consistent with the data. Thus, lensing adds to the evidence that CDM mass distributions are too concentrated on kiloparsec scales to agree with real galaxies, and extends the argument to elliptical galaxies. By contrast, the lack of central images in radio lenses implies that the central densities of CDM galaxies are too low on ~10 parsec scales, even if supermassive black holes are included. Self-interacting dark matter, or any other modification to regular cold dark matter, must simultaneously reduce the densities on kiloparsec scales and increase the densities on parsec scales in order to satisfy the unique constraints from lensing.