  We study the time variation of the apparent flux of cosmological point
sources due to the transient weak lensing by dark matter microhaloes. Assuming
a transverse motion of microhaloes with respect to our line of sight, we derive
the correspondence between the temporal power spectrum of the weak lensing
magnification, and the spatial power spectrum of density on small scales.
Considering different approximations for the small scale structure of dark
matter, we predict the apparent magnitude of cosmological point sources to vary
by as much as $10^{-4}-10^{-3}$, due to this effect, within a period of a few
months. This red photometric noise has an almost perfect gaussian statistics,
to one part in $\sim 10^4$. We also compare the transient weak lensing power
spectrum with the background effects such as the stellar microlensing on
cosmological scales. A quasar lensed by a galaxy or cluster like SDSSJ1004+4112
strong lensing system, with multiple images, is a suitable system for this
study as: (i) using the time-delay method between different images, we can
remove the intrinsic variations of the quasar, and (ii) strong lensing enhances
signals from the transient weak lensing. We also require the images to form at
large angular separations from the center of the lensing structure, in order to
minimize contamination by the stellar microlensing. With long-term monitoring
of quasar strong lensing systems with a 10-meter class telescope, we can
examine the existence of dark microhaloes as the building blocks of dark matter
structures. Failure to detect this signal may either be caused by a breakdown
of cold dark matter (CDM) hierarchy on small scales, or rather interpreted as
evidence against CDM paradigm, e.g. in favor of modified gravity models.
