We perform an analysis of the single white dwarf and the double degenerate binary populations in the solar neighbourhood following a population synthesis approach to investigate the effects of unresolved double degenerates in the white dwarf luminosity function. We consider all unresolved synthetic binaries to be associated with fictitious effective temperatures and surface gravities that are obtained in the same way as if these objects were observed as single point sources. We evaluate the effects of unresolved double white dwarfs assuming that the synthetic samples are observed both by the magnitude-limited SDSS and the volume-limited Gaia surveys, the latter limited to a distance of no more than 100pc. We find that, for our standard model, the impact of unresolved double degenerates in the white dwarf luminosity function derived from the Gaia sample is nearly negligible. Unresolved double degenerates are hence expected to have no effect on the age of the Galactic disc, nor on the star formation history from this population. However, for the SDSS sample, the effect of unresolved double degenerates is significant at the brighter bins (Mbol<6.5 mag), with the fraction of such systems reaching ~40% of the total white dwarf population at Mbol=6 mag. This indicates unresolved double degenerates may influence the constraints on the star formation history derived from the SDSS white dwarf sample.
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