The joint statistics of mildly non-linear cosmological densities and slopes in count in cells

In the context of count-in-cells statistics, the joint probability distribution of the density in two concentric spherical shells is predicted from first principle for sigmas of the order of 1. The agreement with simulation is found to be excellent. This statistics allows us to deduce the conditional one dimensional probability distribution function of the slope within under dense (resp. overdense) regions, or of the density for positive or negative slopes. The former conditional distribution is likely to bemore robust in constraining the cosmological parameters as the underlying dynamics is less evolved in such regions. A fiducial dark energy experiment is implemented on such counts derived from Δ cold dark matter simulations.