Slow-roll Natural & Hilltop Inflation in Rastall Gravity
Isaac M. Vitohekpon, Biswajit Deb, Ines G. Salako, V. A. Monwanou, Atri Deshamukhya
TL;DR
This work analyzes slow-roll inflation within Rastall gravity, examining power-law, natural, and hilltop potentials under minimal matter--gravity coupling. By deriving Rastall-modified slow-roll parameters $\tilde{\epsilon}$, $\tilde{\epsilon}_{V}$, $\tilde{\eta}$, and $\tilde{\eta}_{V}$ and the corresponding e-folds $\tilde{N}$, the authors compute the observable indices $n_s$, $n_T$, and $r$ and map their trajectories in the $(n_s,r)$ plane. Key findings show that, in the power-law case, only $n=\tfrac{2}{3}$ and $n=1$ satisfy Planck 2018 bounds (with specific ranges for the Rastall parameter $\lambda_{\mathrm{Ras}}$); natural inflation's viability depends crucially on the scale $f$, with $f=5M_p$ or $f=10M_p$ fitting Planck and BK constraints under suitable $\lambda_{\mathrm{Ras}}$ ranges, while hilltop models largely fail except for a marginal $m=\tfrac{3}{2}$ case under restricted conditions. Overall, the paper demonstrates that Rastall gravity can reproduce inflation compatible with observations, but only within narrowly defined parameter spaces and model choices, highlighting the interplay between modified gravity and early-universe phenomenology.
Abstract
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 $n = 2/3$ 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 $m = 3/2, 2, 3$, and $4$, only $m = 3/2$ exhibits marginal consistency with observational bounds, while the other cases fail to produce acceptable $(n_s - r)$ trajectories.