Fresh inflation with increasing cosmological parameter

I study a fresh inflationary model with an increasing F-cosmological parameter. The model provides sufficiently e-folds to solve the flatness/horizon problem and the density fluctuations agree with experimental values. The temperature increases during fresh inflation and reach its maximum value when inflation ends. I find that entropy perturbations always remain below ${10}^{-4}$ during fresh inflation and become negligible when fresh inflation ends. Hence, the adiabatic fluctuations dominate the primordial spectrum at the end of fresh inflation.