International audienceA large-deviation principle is used to model the time-evolution of the large-scale structure of the Universe. This approach allows for analytical predictions in the mildly non-linear regime, beyond what is commonly achievable via other statistics such as correlation functions. The idea is to measure the mean cosmic densities within concentric spheres and study their joint statistics.The spherical symmetry then leads to surprisingly accurate predictions where standard calculations of perturbation theory usually break down. Results for the one-point statistics of the cosmic density field are shown and implications for future large galaxy surveys are discussed