  Through its connection with HED meteorites, Vesta is known as one of the
first bodies to have accreted and differentiated in the Solar Nebula, predating
the formation of Jupiter and surviving the violent evolution of the early Solar
System. The formation time of Ceres instead is unknown, but it should not
postdate that of Jupiter by far. In this work we modelled the collisional
histories of Vesta and Ceres at the time of the formation of Jupiter, assumed
to be the first giant planet to form. In this first investigation of the
evolution of the early Solar System, we did not include the presence of
planetary embryos in the disk of planetesimals but we concentrated on the role
of the forming Jupiter and the effects of its possible inward migration due to
disk-planet interactions. Our results clearly indicate that the formation of
the giant planet caused an intense early bombardment in the orbital region of
the Main Asteroid Belt. According to our results, Vesta and Ceres would not
have survived the Jovian early bombardment if the disk was populated mainly by
large planetesimals like those predicted to form in turbulent circumstellar
disks. Disks dominated by small bodies, like those predicted to form in
quiescent circumstellar disks, or with a varying fraction of the mass in the
form of larger (D \geq 100 km) planetesimals represent more favourable
environments for the survival of the two asteroids. In those scenarios where
they survive, both asteroids had their surfaces saturated by craters as big as
150 km and a few as big as 200 - 300 km. In the case of Vesta, the Jovian early
bombardment would have significantly eroded (locally or globally) the crust and
possibly caused effusive phenomena similar to the lunar maria, whose
crystallisation time would then be directly linked to the time of the formation
of Jupiter.
