Radiatively Corrected Hybrid Inflation: Parameter Scans and Machine Learning with ACT and Future CMB Experiments

We investigate a realistic non-supersymmetric hybrid inflation model incorporating right-handed neutrinos and assess its viability in light of recent cosmological observations. At tree level, the inflaton potential yields a blue-tilted scalar spectrum, which is disfavored by current data from Planck and ACT that instead support a red tilt. We show that including one-loop quantum corrections, arising from generic couplings required for reheating, significantly modifies the potential, flattening it at large field values. This leads to a red-tilted spectral index ($n_s < 1$) and a suppressed tensor-to-scalar ratio $r$, both consistent with observational constraints. To ensure theoretical control, we focus on sub-Planckian field values, where the effective field theory description remains valid. The coupling of the inflaton to right-handed neutrinos naturally facilitates efficient reheating and enables the generation of the baryon asymmetry via non-thermal leptogenesis. We further explore the model's parameter space using a multi-output random forest classifier, achieving prediction accuracies in the range of $87.5\%$ to $98.9\%$. Our analysis shows that approximately $15\%$ of the parameter space satisfies at least one current experimental constraint, underscoring the essential role of quantum corrections in reconciling particle physics models with precision cosmology, and highlighting the effectiveness of machine learning techniques in probing complex theoretical frameworks.