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 .