A single field inflationary potential consistent with recent observations

TL;DR

This work introduces a simple single-field inflation model based on an inverse-exponential potential $V(\phi)=V_0\,e^{-\alpha M_{\rm Pl}/\phi}$, showing it yields a small tensor-to-scalar ratio $r$ and a scalar spectral index $n_s$ around $0.97$ that are compatible with the SPA+BK+DESI2 constraints across a broad range of $\alpha$. It then extends the potential to $V(\phi)=V_0\big(e^{-\alpha M_{\rm Pl}/\phi}+e^{-\beta \phi/M_{\rm Pl}}\big)$ to generate a post-inflation minimum at $\phi_{eq}=\sqrt{\alpha/\beta}\,M_{\rm Pl}$, enabling reheating via inflaton oscillations; consistency with observations constrains $\beta$ to exceed $\sqrt{2}$ and yields a maximum reheating temperature of order $10^{12}$–$10^{13}$ GeV. The analysis uses the slope and curvature parameters $\lambda=\alpha/\phi^2$ and $\Gamma=1-2\phi/\alpha$ to characterize inflation and demonstrates that the model sits comfortably within current data, with negligible running $\alpha_s$ over the viable parameter space. Overall, the paper presents a minimal, observationally robust inflationary scenario that naturally connects to reheating and offers a compelling anti-tracker perspective on concave potentials.

Abstract

Current observations indicate that an inverse exponential form of the inflaton potential provides an excellent description of single-field inflation. This potential fits the SPA$+$BK$+$DESI data sets well with in the $1σ$ bound in the $n_{\rm s}$-$r$ plane, thereby offering a simple and observationally viable single field inflationary scenario. To describe post-inflationary evolution and reheating, we extend the inverse exponential potential by adding a steep exponential term that remains negligible during inflation but becomes important afterwards. The resulting full potential develops a minimum after the end of inflation, leading to oscillations of the scalar field and consequently reheating of the Universe. We find that the maximum reheating temperature attainable in this scenario is of order $10^{13}\,\mathrm{GeV}$. The inverse exponential potential therefore emerges as a compelling candidate for early-Universe inflation, combining theoretical simplicity with robust observational viability.

Figures (7)

• Figure 1: Nature of the potential \ref{['eq:potential_inflation']} and its slope ($\lambda$) and curvature ($\Gamma$) for $\phi/M_{\rm Pl} > 0$ with $\alpha = 1$.
• Figure 2: Inflation parameters for the potential \ref{['eq:potential_inflation']} for $\phi/M_{\textrm{Pl}}>0$. For all the plots $0.05 \leq \alpha \leq 10$.
• Figure 3: Comparison of the theoretical prediction of tensor-to-scalar ratio $r$ and the scalar spectral index $n_{\rm s}$ with the observational results for $N_\star=50$--$60$. In the upper figure, along with our model we have also shown the predictions from the $R^2$ Starobinsky inflationary model and monomial inflationary model. The bottom figure shows a magnified view of the upper panel, highlighting the predictions of our model for $N_\star=50$–$60$. For the contours we use publicly available MCMC chains Balkenhol:2025wms.
• Figure 4: Nature of the full inflationary potential \ref{['eq:potential_full']} for $\alpha=1$ and $\beta=15$.
• Figure 5: Post-inflationary evolution of the scalar field for the potential \ref{['eq:potential_full']} for $\alpha=1$ and $\beta=30$.