  A log Gaussian Cox process (LGCP) is a doubly stochastic construction
consisting of a Poisson point process with a random log-intensity given by a
Gaussian random field. Statistical methodology have mainly been developed for
LGCPs defined in the $d$-dimensional Euclidean space. This paper concerns the
case of LGCPs on the $d$-dimensional sphere, with $d=2$ of primary interest. We
discuss the existence problem of such LGCPs, provide sufficient existence
conditions, and establish further useful theoretical properties. The results
are applied for the description of sky positions of galaxies, in comparison
with previous analysis based on a Thomas process, using simple estimation
procedures and making a careful model checking. We account for inhomogeneity in
our models, and as the model checking is based on a thinning procedure which
produces homogeneous/isotropic LGCPs, we discuss its sensitivity.
