(abridged)We present a model which predicts inflation without the presence of inflaton fields, based on the ��R^2 and Starobinsky models. It links the above models to the observable universe, in particular, to the ratio r of tensor to scalar fluctuations. In our model, we assume the existence of particles with the mass M that have a long decay time. These particles which were gravitationally produced \sim 60e-folds before the end of inflation produced the nearly scale invariant scalar density fluctuations which are observed. Gravitational waves (tensor fluctuations) were also produced at this epoch. The ratio of tensor to scalar fluctuations r (which are to be measured in the near future to good accuracy) determines M, which together with H_0, determine the time at the end of inflation, t_end. At t_end, the Hubble parameter begins to oscillate rapidly, gravitationally producing the bulk of the M particles, which we identify with the matter content of the universe today. The time required for the universe to dissipate its vacuum energy into M particles is found to be t_dis \simeq 6M_Pl^2/M^3. We assume that the time t_RH, (called the reheating time) needed for the M particles to decay into relativistic particles, is very much greater than that necessary to create the M particles, t_dis. From the ratio f\equiv t_dis/t_RH and g_\ast (the total number of degrees of freedom of the relativistic particles) we can, then, evaluate the maximum temperature of the universe, T_max, and the reheat temperature, T_RH, at t_RH. Our model, thus, predicts M, t_dis, t_end, T_max, T_RH, t_max, and t_RH as a function of r, f, and g_\ast (and to a weaker extent the particle content of the vacuum near the Planck epoch).

11 pages, 2 figures. Revised version, accepted for publication in Phys. Rev. D