Revisiting Polynomial Hybrid Inflation: Planck and ACT Compatibility via Radiative Corrections

Abstract

We investigate the impact of one-loop radiative corrections in a non-supersymmetric model of hybrid inflation with a chaotic (polynomial-like) potential,$V(φ) = V_0 + λ_p φ^p$, in the light of the latest constraints from \textit{Planck} and \textit{Atacama Cosmology Telescope} (ACT) observations. Here, $V_0$ denotes the energy scale of inflation, and $λ_p$ is a coupling associated with the polynomial term of power $p$. These corrections can naturally arise from couplings of the inflaton to other matter fields, which also facilitate the reheating process. At the tree level, the predictions of such models for the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ typically lie outside the current observational bounds. However, incorporating one-loop radiative corrections modifies the potential to, \[ V(φ) = V_0 + λ_p φ^p + A φ^4 \ln (φ/ μ), \] where $A$ characterizes the strength of the inflaton's coupling to other fields, and \(μ\) is an appropriate renormalization scale. This radiatively corrected potential can reconcile the model with the combined \textit{Planck}+ACT data over a suitable range of parameter space explored in this work. In particular, radiative corrections from fermionic loops ($A < 0$) suppress the tensor-to-scalar ratio $r$, while simultaneously yielding a red-tilted spectrum with $n_s < 1$, even for sub-Planckian field excursions. This brings the prediction in line with current observations, while still allowing for potentially detectable signatures of primordial gravitational waves. Furthermore, the inflaton's couplings enable successful reheating and naturally accommodate non-thermal leptogenesis, providing a unified framework for inflation and baryogenesis.

Figures (4)

• Figure 1: The tensor-to-scalar ratio $r$ is plotted against the scalar spectral index $n_s$, with the black dashed and solid contours indicating the $1\sigma$ and $2\sigma$ confidence regions derived from the combined Planck 2018, ACT DR6, and BICEP/Keck 2018 datasets (P+ACT+LB+BK18) AtacamaCosmologyTelescope:2025nti. The small and large blue dots correspond to predictions for $N = 50$ and $N = 60$$e$-folds, respectively. The solid lines represent predictions from the radiatively corrected potential with fermionic loops ($A<0$), whereas the dashed lines correspond to the bosonic correction scenario ($A>0$).
• Figure 2: The left panel illustrates the tensor-to-scalar ratio $r$ versus the scalar spectral index $n_s$, where the color coding represents the radiative correction parameter $A$, showcasing its influence on inflationary predictions. Overlaid are the 1$\sigma$ (dotted) and 2$\sigma$ (dashed) confidence contours derived from the combined datasets of Planck 2018, ACT DR6, and BICEP/Keck 2018 (P + ACT + LB + BK18) AtacamaCosmologyTelescope:2025nti. The right panel shows the running of the scalar spectral index $\alpha_s$ against the parameter $\kappa = g$, with color coding indicating the number of e-folds $N_0$.
• Figure 3: The left panel shows the coupling constant $\lambda_p^{\frac{1}{4-p}}$ versus the symmetry breaking scale $M$, with color coding representing the field value $\phi_0$. The right panel presents the inflaton mass $m_\phi = m_{\chi}$ as a function of the reheating temperature $T_r$, where the color coding indicates the lightest right-handed neutrino mass scale $M_N$. All the data points shown in the rain bow color satisfy the observational constraints on the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ from Planck 2018, ACT DR6, and BICEP/Keck 2018 (P + ACT + LB + BK18) AtacamaCosmologyTelescope:2025nti.
• Figure 4: Predicted values of the scalar spectral index $n_s$ and its running $\alpha_s \equiv d n_s / d\ln k$ for radiatively corrected hybrid inflation with chaotic polynomial potentials of powers $p = 1$, $2/3$, and $1/3$ (from the upper-left to the lower panels), compared with the 1$\sigma$ and 2$\sigma$ confidence regions from the latest combined Planck 2018 and ACT DR6 data (P–ACT–LB) AtacamaCosmologyTelescope:2025nti. .