A single field inflationary potential consistent with recent observations

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.

💡 Research Summary

The paper addresses the growing tension between recent high‑precision cosmological observations and traditional single‑field inflationary models. Combining data from Planck 2018, ACT DR6, DESI DR1/DR2, SPT‑3G, and BICEP/Keck, the authors note that the scalar spectral index ns has shifted upward to values around 0.97, while the tensor‑to‑scalar ratio r is constrained to be below about 0.035. In this context, classic models such as Starobinsky’s R² inflation or simple monomial potentials (ϕⁿ) struggle to remain within the 2σ confidence region, especially for the preferred number of e‑folds N≈50–60.

Motivated by this, the authors propose an “inverse exponential” (IExp) potential of the form
 V(ϕ)=V₀ exp(−α Mₚₗ/ϕ),
where α is a dimensionless parameter and Mₚₗ is the reduced Planck mass. This potential is monotonic for ϕ>0 and yields simple slow‑roll parameters: ε_V∝α²/ϕ⁴ and η_V∝α/ϕ³−2α²/ϕ⁴. Inflation ends when ε_V=1, giving ϕ_end≈α^{1/2} Mₚₗ. The number of e‑folds between horizon exit (ϕ_*) and the end of inflation is N≈(ϕ_³−ϕ_end³)/(3α Mₚₗ³), which for N≫α reduces to ϕ_≈(3αN)^{1/3} Mₚₗ.

Evaluating the observable quantities at ϕ_* leads to
 r=8α² Mₚₗ⁴/ϕ_*⁴, ns=1−α² Mₚₗ⁴/ϕ_*⁴−4α Mₚₗ³/ϕ_*³.
Scanning α in the range 0.05–10, the model predicts r≈10⁻³–10⁻² and ns≈0.965–0.978 for N=50–60. Notably, for α≈1 the predictions ns≈0.972 and r≈0.004 sit squarely inside the 1σ contour of the combined ACT‑BK‑DESI2 data set. By contrast, the R² model and the monomial potentials lie partially or entirely outside the 2σ region, highlighting the superior fit of the IExp form.

A technical issue arises because V(ϕ) diverges as ϕ→0, which would prevent a graceful exit and reheating. To resolve this, the authors augment the potential with a steep exponential term that is negligible during inflation but dominates afterward:
 V(ϕ)=V₀