The Starobinsky model predicts a primordial inflation period without the presence of an inflaton field. The modified version of this model predicts a simple time dependence for the Hubble parameter H(t), which decreases slowly between the Planck epoch and the end of the inflation, H(t) = M Pl -betaM²Pl t, where beta is a dimensionless constant to be adjusted from observations. We investigate an inflaton model which has the same time dependence for H(t). A reverse engineered inflaton potential for the time dependence of H is derived. Normalization of the derived inflaton potential is determined by the condition that the observed density fluctuations, <FONT FACE=Symbol>dr</FONT>/<FONT FACE=Symbol>r »</FONT> 10-5, are created at ~ 60 e-folds before the end of inflation. The derived potential indicates an energy (mass) scale, Mend ~ 10(13) GeV, at the end of inflation. Using the slow roll parameters, which are obtained from this potential, we calculate the spectral index for the scalar modes nS and the relative amplitude of the tensor to scalar modes r. A tensor contribution, r ~ 0.13, and an approximately Harrison-Zeldovich density perturbation spectrum, nS ~ 0.95, are predicted.
Inflation model; Planck epoch; Inflaton model
