Observational constraints on the sub-galactic matter-power spectrum from
  galaxy-galaxy strong gravitational lensing
  Constraining the sub-galactic matter-power spectrum on 1-10 kpc scales would
make it possible to distinguish between the concordance $\Lambda$CDM model and
various alternative dark-matter models due to the significantly different
levels of predicted mass structure. Here, we demonstrate a novel approach to
observationally constrain the population of overall law-mass density
fluctuations in the inner regions of massive elliptical lens galaxies, based on
the power spectrum of the associated surface-brightness perturbations
observable in highly magnified galaxy-scale Einstein rings and gravitational
arcs. The application of our method to the SLACS lens system SDSS J0252+0039
results in the following limits (at the 99 per cent confidence level) on the
dimensionless convergence-power spectrum (and the associated standard deviation
in aperture mass): $\Delta^{2}_{\delta\kappa}<1$ ($\sigma_{AM}< 0.8 \times 10^8
M_\odot$) on 0.5-kpc scale, $\Delta^{2}_{\delta\kappa}<0.1$ ($\sigma_{AM}< 1
\times 10^8 M_\odot$) on 1-kpc scale and $\Delta^{2}_{\delta\kappa}<0.01$
($\sigma_{AM}< 3 \times 10^8 M_\odot$) on 3-kpc scale. The estimated effect of
CDM sub-haloes lies considerably below these first observational upper-limit
constraints on the level of inhomogeneities in the projected total mass
distribution of galactic haloes. Future analysis for a larger sample of
galaxy-galaxy strong lens systems will narrow down these constraints and rule
out all cosmological models predicting a significantly larger level of
clumpiness on these critical sub-galactic scales.
