Lensing dispersion of supernova flux: a probe of non-linear structure growth

The scatter in the apparent magnitude of Type Ia supernovae induced by stochastic gravi- tational lensing is highly dependent on the non-linear growth of cosmological structure. In this paper, we show that such a dependence can potentially be employed to gain significant information about the mass clustering at small scales. While the mass clustering ultimately hinges on cosmology, here we demonstrate that, upon obtaining more precise observational measurements through future cosmological surveys, the lensing dispersion can very effec- tively be used to gain information on the poorly understood astrophysical aspects of structure formation, such as the clumpiness of dark matter haloes and the importance of gas physics and star formation into shaping the large-scale structure. In order to illustrate this point, we verify that even the tentative current measurements of the lensing dispersion performed on the Supernova Legacy Survey sample favour a scenario where virialized structures are somewhat less compact than predicted by N-body cosmological simulations. Moreover, we are also able to put lower limits on the slope of the concentration–mass relation. By artificially reducing the statistical observational error, we argue that with forthcoming data the stochastic lensing dispersion will allow one to importantly improve constraints on the baryonic physics at work during the assembly of cosmological structure.