One of the most promising space missions of ESA is the astrometric satellite
Gaia, which will provide very precise astrometry and multicolour photometry,
for all 1.3 billion objects to V~20, and radial velocities with accuracies of a
few km/s for most stars brighter than V ~ 17. Consequently, full homogeneous
six-dimensional phase-space information for a huge number of stars will become
available. Our Monte Carlo simulator has been used to estimate the number of
white dwarfs potentially observable by Gaia. From this we assess which would be
the white dwarf luminosity functions which Gaia will obtain and discuss in
depth the scientific returns of Gaia in the specific field of white dwarf
populations. Scientific attainable goals include, among others, a reliable
determination of the age of the Galactic disk, a better knowledge of the halo
of the Milky Way and the reconstruction of the star formation history of the
Galactic disk. Our results also demonstrate the potential impact of a mission
like Gaia in the current understanding of the white dwarf cooling theory.Comment: 13 pages, 17 figures, accepted for publication in MNRA