Large deviation principle at play in large scale structure cosmology

We present an application of large deviation theory to the problem of structure growth on large scale structure cosmology. Starting from Gaussian distributed overdensities on concentric spherical shells, we show that a large deviation principle holds for the densities on the corresponding shells after gravitational evolution if no shell crossing happens. As consequences of the large deviation principle we obtain the cumulant-generating function for the nonlinear densities, and present formulas to compute the cumulant-generating function for general window functions.