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We devise an optimal method to measure the temporal power spectrum of thelensing and intrinsic fluctuations of multiply-imaged strongly lensed quasarlight curves, along with the associated time delays. The method is based on aMonte-Carlo Markov Chain (MCMC) sampling of a putative gaussian likelihood, andaccurately recovers the input properties of simulated light curves, as well asthe "Time Delay Challenge". We apply this method to constrain the dimensionlesscosmological (non-linear) matter power spectrum on milliparsec scales(comparable to the size of the solar system), to $\Delta_{\rm NL}^2< 4 \times10^7$ at $k_{\rm NL} \sim 10^3 {\rm pc}^{-1}$. Using a semi-analytic nonlinearclustering model which is calibrated to simulations, the correspondingconstraint on the primordial (linear) scalar power spectrum is ${\cal P}_{\calR} < 3 \times 10^{-9}$ at $k_{\rm L}\sim$ 3 pc$^{-1}$. This is the strongestconstraint on primordial power spectrum at these scales, and is within an orderof magnitude from the standard $\Lambda$CDM prediction. We also reportmeasurements of temporal spectra for intrinsic variabilities of quasar lightcurves, which can be used to constrain the size of the emitting region inaccretion disks. Future cadenced optical imaging surveys, such as LSST, shouldincrease the number of observed strongly lensed quasars by 3 orders ofmagnitude and significantly improve these measurements, even thoughimprovements in modelling quasar accretion and stellar microlensing arenecessary.

Forward modelling of quasar light curves and the cosmological matter power spectrum on milliparsec scales