A Geometric Probe of Cosmology: I. Gravitational Lensing Time Delays and
  Quasar Reverberation Mapping
  We present a novel, purely geometric probe of cosmology based on measurements
of differential time delays between images of strongly lensed quasars due to
finite source effects. Our approach is solely dependent on cosmology via a
ratio of angular diameter distances, the image separation, and the source size.
It thereby entirely avoids the challenges of lens modelling that conventionally
limit time delay cosmography, and instead entails the lensed reverberation
mapping of the quasar Broad Line Region. We demonstrate that differential time
delays are measurable with short cadence spectroscopic monitoring of lensed
quasars, through the timing of kinematically identified features within the
broad emission lines. This provides a geometric determination of an angular
diameter distance ratio complementary to standard probes, and as a result is a
potentially powerful new method of constraining cosmology.
