  In a series of two papers, we test the primordial scenario of globular
cluster formation using results of high-resolutions N-body simulations. In this
first paper we study the initial relaxation of a stellar core inside a live
dark matter minihalo in the early universe. Our dark-matter dominated globular
clusters show features which are usually attributed to the action of the tidal
field of the host galaxy. Among them are the presence of an apparent cutoff
("tidal radius") or of a "break" in the outer parts of the radial surface
brightness profile, and a flat line-of-sight velocity dispersion profile in the
outskirts of the cluster. The apparent mass-to-light ratios of our hybrid
(stars + dark matter) globular clusters are very close to those of purely
stellar clusters. We suggest that additional observational evidence such as the
presence of obvious tidal tails is required to rule out the presence of
significant amounts of dark matter in present day globular clusters.
