g}$, and the left panel of Figure \[g-eps\] shows how these two quantities are related for $N=50$ and $N=60$. In the right panel of the Figure we show instead how the initial value of the slow roll parameter $\epsilon$ is related to $\gamma_{\rm in}$.

![Left panel: Relation between the dimensionless parameter ${\tilde g} \equiv \sqrt{\kappa} M_p^2 g $, and the initial value of $\gamma $, for $N=50$ and $N=60$ e-folds of inflation. The quantities $N$ and $\gamma_{\rm in}$ completely characterize the model and the background evolution. Right panel: relation between the initial value of the slow roll parameter $\epsilon$ and of $\gamma$. \[g-eps\]](g-vs-gamma "fig:"){width="45.00000%"} ![Left panel: Relation between the dimensionless parameter ${\tilde g} \equiv \sqrt{\kappa} M_p^2 g $, and the initial value of $\gamma $, for $N=50$ and $N=60$ e-folds of inflation. The quantities $N$ and $\gamma_{\rm in}$ completely characterize the model and the background evolution. Right panel: relation between the initial value of the slow roll parameter $\epsilon$ and of $\gamma$. \[g-eps\]](eps-vs-gamma "fig:"){width="45.00000%"}

In Figure \[fig:Q-eps-bck\], we show both the inflationary evolution of $Q(t)$ (left panel) and of the slow roll parameter $\epsilon$ (right panel), for $60$ e-folds of inflation and for two values of the parameter $\gamma$. Solid 