  Recent models of solar system formation suggest that a dynamical instability
among the giant planets happened within the first 100 Myr after disk dispersal,
perhaps before the Moon-forming impact. As a direct consequence, a bombardment
of volatile-rich impactors may have taken place on Earth before internal and
atmospheric reservoirs were decoupled. However, such a timing has been
interpreted to potentially be at odds with the disparate inventories of Xe
isotopes in Earth's mantle compared to its atmosphere. This study aims to
assess the dynamical effects of an Early Instability on the delivery of
carbonaceous asteroids and comets to Earth, and address the implications for
the Earth's volatile budget. We perform 20 high-resolution dynamical
simulations of solar system formation from the time of gas disk dispersal, each
starting with 1600 carbonaceous asteroids and 10000 comets, taking into account
the dynamical perturbations from an early giant planet instability. Before the
Moon-forming impact, the cumulative collision rate of comets with Earth is
about 4 orders of magnitude lower than that of carbonaceous asteroids. After
the Moon-forming impact, this ratio either decreases or increases, often by
orders of magnitude, depending on the dynamics of individual simulations. An
increase in the relative contribution of comets happens in 30\% of our
simulations. In these cases, the delivery of noble gases from each source is
comparable, given that the abundance of 132Xe is 3 orders of magnitude greater
in comets than in carbonaceous chondrites. The increase in cometary flux
relative to carbonaceous asteroids at late times may thus offer an explanation
for the Xe signature dichotomy between the Earth's mantle and atmosphere.
