Slow-roll Natural & Hilltop Inflation in Rastall Gravity

This study provides a concise analysis of inflation under Rastall gravity by examining three types of potential such as the power law, natural, and hilltop potentials. Choosing a minimal interaction between matter and gravity, we derived the modified slow-roll parameters, the scalar spectral index $(n_s)$, the tensor spectral index $(n_T)$, and the tensor-to-scalar ratio $(r)$. For a general power-law potential as well as for Natural & Hilltop inflation, we calculated these quantities and subsequently plotted their trajectories in the $(n_s,r)$ plane. For the power-law potential, only the cases $n=2\mathrm{/}3$ and $n=1$ satisfy the observational constraint of the Planck 2018 data. The natural potential analysis shows that the mass scale is crucial, with better compatibility achieved at $f=5M_p$ compared to $f=10M_p$. Lastly, the Hilltop potential results indicate that among the cases studied $m=3\mathrm{/}2,2,3$, and $4$, only $m=3\mathrm{/}2$ exhibits marginal consistency with observational bounds, while the other cases fail to produce acceptable $(n_s-r)$ trajectories.