  Comets are considered a potential source of inner solar system volatiles, but
the timing of this delivery relative to that of Earth's accretion is still
poorly understood. Measurements of xenon isotopes in comet
67P/Churyumov-Gerasimenko revealed that comets partly contributed to the
Earth's atmosphere. However, there is no conclusive evidence of a significant
cometary component in the Earth's mantle. These geochemical constraints would
favour a contribution of comets mainly occurring after the last stages of
Earth's formation. Here, we evaluate whether dynamical simulations satisfy
these constraints in the context of an Early Instability model. We perform
dynamical simulations of the solar system, calculate the probability of
collision between comets and Earth analogs component embryos through time and
estimate the total cometary mass accreted in Earth analogs as a function of
time. While our results are in excellent agreement with geochemical
constraints, we also demonstrate that the contribution of comets on Earth might
have been delayed with respect to the timing of the instability, due to a
stochastic component of the bombardment. More importantly, we show that it is
possible that enough cometary mass has been brought to Earth after it had
finished forming so that the xenon constraint is not necessarily in conflict
with an Early Instability scenario. However, it appears very likely that a few
comets were delivered to Earth early in its accretion history, thus
contributing to the mantle's budget. Finally, we compare the delivery of
cometary material on Earth to Venus and Mars. These results emphasize the
stochastic nature of the cometary bombardment in the inner solar system.
