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We use Gaia DR2 magnitudes, colours and parallaxes for stars with G<12 toexplore a 15-dimensional space that includes simultaneously the initial massfunction (IMF) and a non-parametric star formation history (SFH) for theGalactic disc. This inference is performed by combining the Besancon GalaxyModel fast approximate simulations (BGM FASt) and an approximate Bayesiancomputation algorithm. We find in Gaia DR2 data an imprint of a star formationburst 2-3 Gyr ago, in the Galactic thin disc domain, and a present starformation rate (SFR) of about 1 Msun. Our results show a decreasing trend ofthe SFR from 9-10 Gyr to 6-7 Gyr ago. This is consistent with the cosmologicalstar formation quenching observed at redshifts z<1.8. This decreasing trend isfollowed by a SFR enhancement starting at about 5 Gyr ago and continuing untilabout 1 Gyr ago which is detected with high statistical significance bydiscarding the null hypothesis of an exponential SFH with a p-value=0.002. Weestimate, from our best fit model, that about the 50% of the mass used togenerate stars, along the thin disc life, was expended in the period from 5 to1 Gyr ago. The timescale and the amount of stellar mass generated during theSFR enhancement event lead us to hypothesise that its origin, currently underinvestigation, is not intrinsic to the disc. Thus, an external perturbation isneeded for its explanation. Additionally we find, for the thin disc, a slope ofthe IMF of $\alpha_3 \approx 2$ for masses M>1.53 Msun and $\alpha_2 \approx1.3$ for the mass range between 0,5 and 1,53 Msun. This is the first time thatwe consider a non-parametric SFH for the thin disc in the Besancon GalaxyModel. This new step, together with the capabilities of the Gaia DR2 parallaxesto break degeneracies between different stellar populations, allow us to betterconstrain the SFH and the IMF.

Gaia DR2 reveals a star formation burst in the disc 2-3 Gyr ago