  We consider the effects of adding a scale invariant $R^{2}$ term to the
action of the scale invariant model (SIM) studied previously by one of us
(E.I.G., Mod. Phys. Lett. A14, 1043 (1999)). The SIM belongs to the general
class of theories, where an integration measure independent of the metric is
introduced. To implement scale invariance (S.I.), a dilaton field is
introduced. The integration of the equations of motion associated with the new
measure gives rise to the spontaneous symmetry breaking (S.S.B) of S.I.. After
S.S.B. of S.I. in the model with the $R^{2}$ term, it is found that a non
trivial potential for the dilaton is generated. This potential contains two
flat regions: one associated with the Planck scale and with an inflationary
phase, while the other flat region is associated to a very small vacuum energy
(V.E.) and is associated to the present slowly accelerated phase of the
universe (S.A.PH). The smallness of the V.E. in the S.A.PH. is understood
through the see saw mechanism introduced in S.I.M.
