  We investigate the pair creation of noncommutative black holes in a
background with positive cosmological constant. As a first step we derive the
noncommutative geometry inspired Schwarzschild deSitter solution. By varying
the mass and the cosmological constant parameters, we find several spacetimes
compatible with the new solution: positive mass spacetimes admit one
cosmological horizon and two, one or no black hole horizons, while negative
mass spacetimes have just a cosmological horizon. These new black holes share
the properties of the corresponding asymptotically flat solutions, including
the non-singular core and thermodynamic stability in the final phase of the
evaporation. As a second step we determine the action which generates the
matter sector of gravitational field equations and we construct instantons
describing the pair production of black holes and the other admissible
topologies. As a result we find that for current values of the cosmological
constant the deSitter background is quantum mechanically stable according to
experience. However positive mass noncommutative black holes and solitons would
have plentifully been produced during inflationary times for Planckian values
of the cosmological constant. As a special result we find that, in these early
epochs of the universe, Planck size black holes production would have been
largely disfavoured. We also find a potential instability for production of
negative-mass solitons.
