Probing Reheating in a Decaying Oscillatory Inflationary Model with Latest ACT Constraints

Abstract: Recent observations from the Atacama Cosmology Telescope (ACT) indicate a moderate upward shift in the scalar spectral index $n_s$ compared to Planck $2018$, thereby placing tighter constraints on inflationary scenarios. Motivated by these results, we investigate a decaying oscillatory Inflationary model inspired by minimal no-scale supergravity, characterized by the potential $V(\phi) = \lambda \phi^{2n} \sin^2(l/\phi^n)$. We perform a numerical analysis of the background dynamics and reheating process across a range of model parameters. The model yields robust predictions for $n_s$ and the tensor-to-scalar ratio $r$, in excellent agreement with current ACT data. Successful reheating in this model requires a large effective equation-of-state parameter approaching unity, consistent with both cosmic microwave background (CMB) and big bang nucleosynthesis (BBN) constraints. The corresponding number of inflationary $e$-folds increases with $n$ and is weakly sensitive to $l$. Overall, the model offers a simple yet predictive framework that captures both inflationary dynamics and post-inflationary reheating, and remains viable under the latest high-precision observations.