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The scatter in the apparent magnitude of type Ia supernovae induced bystochastic gravitational lensing is highly dependent on the nonlinear growth ofcosmological structure. In this paper, we show that such a dependence canpotentially be employed to gain significant information about the massclustering at small scales. While the mass clustering ultimately hinges oncosmology, here we demonstrate that, upon obtaining more precise observationalmeasurements through future cosmological surveys, the lensing dispersion canvery effectively be used to gain information on the poorly understoodastrophysical aspects of structure formation, such as the clumpiness of darkmatter halos and the importance of gas physics and star formation into shapingthe large-scale structure. In order to illustrate this point we verify thateven the tentative current measurements of the lensing dispersion performed onthe Supernova Legacy Survey sample favor a scenario where virialized structuresare somewhat less compact than predicted by $n-$body cosmological simulations.Moreover, we are also able to put lower limits on the slope of theconcentration-mass relation. By artificially reducing the statisticalobservational error we argue that with forthcoming data the stochastic lensingdispersion will allow one to importantly improve constraints on the baryonicphysics at work during the assembly of cosmological structure.

Lensing dispersion of supernova flux: a probe of nonlinear structure growth