  We study a statistical model defined by a conformally invariant distribution
of overlapping spheres in arbitrary dimension d. The model arises as the
asymptotic distribution of cosmic bubbles in d+1 dimensional de Sitter space,
and also as the asymptotic distribution of bubble collisions with the domain
wall of a fiducial "observation bubble" in d+2 dimensional de Sitter space. In
this note we calculate the 2-,3-, and 4-point correlation functions of
exponentials of the "bubble number operator" analytically in d=2. We find that
these correlators, when carefully defined, are free of infrared divergences,
covariant under the global conformal group, charge conserving, and transform
with positive conformal dimensions that are related in a novel way to the
charge. Although by themselves these operators probably do not define a
full-fledged conformal field theory, one can use the partition function on a
sphere to compute an approximate central charge in the 2D case. The theory in
any dimension has a noninteracting limit when the nucleation rate of the
bubbles in the bulk is very large. The theory in two dimensions is related to
some models of continuum percolation, but it is conformal for all values of the
tunneling rate.
