Context: This study has been developed in the framework of the computational simulations that are executed for the preparation of the ESA Gaia astrometric mission. Aims: We focus on describing the objects and characteristics that Gaia will potentially observe without taking into consideration instrumental effects (detection efficiency, observing errors). Methods: The theoretical Universe Model prepared for the Gaia simulation has been statistically analysed at a given time. Ingredients of the model are described, with the greatest emphasis on the stellar content, the double and multiple stars, and variability. Results: In this simulation the errors have not yet been included. Hence we estimated the number of objects and their theoretical photometric, astrometric and spectroscopic characteristics if they are perfectly detected.We show that Gaia will be able to potentially observe 1.1 billion of stars (single or part of multiple star systems) of which about 2% are variable stars and 3% have one or two exoplanets. At the extragalactic level, observations will be potentially composed of several millions of galaxies, half a million to 1 million quasars and about 50,000 supernovae that will occur during the five years of the mission.