  We describe the universe as a local, inhomogeneous spherical bubble embedded
in a flat matter dominated FLRW universe. Generalized exact Friedmann equations
describe the expansion of the universe and an early universe inflationary de
Sitter solution is obtained. A non-perturbative expression for the deceleration
parameter q is derived that can possibly describe the acceleration of the
universe without dark energy, due to the effects associated with very long wave
length super-horizon inflationary perturbations. The suggestion by Kolbe et al.
[9] that long wave length super-horizon inflationary modes can affect a local
observable through inhomogeneities is considered in the light of our exact
inhomogeneous model.
