We define and study the existence of log Gaussian Cox processes (LGCPs) for the description of inhomogeneous and aggregated/clustered point patterns on the $d$-dimensional sphere, with $d=2$ of primary interest. Useful theoretical properties of LGCPs are studied and applied for the description of sky positions of galaxies, in comparison with previous analysis using a Thomas process. We focus on simple estimation procedures and model checking based on functional summary statistics and the global envelope test.

Keywords: Hölder continuity, minimum contrast estimation, model checking, point processes on the sphere, reduced Palm distribution, second order intensity reweighted homogeneity.