The recent measurements from the Atacama Cosmology Telescope (ACT) favor a higher value of the scalar spectral index $n_s$ compared to the Planck data, challenging many well-established inflationary models. In this work, we investigate the viability of polynomial potential inflation in light of the latest ACT data, systematically analyzing cases from $n=2$ to $n=5$. By exploring the parameter space and deriving constraints on the model coefficients, we find that the cubic to quintic models can provide a good fit to the data, while the quadratic model struggles to simultaneously accommodate the ACT data and the requirement of sufficient inflation. Notably, the quintic case ($n=5$) not only matches cosmic microwave background (CMB) observations but also produces an inflection point that simultaneously triggers primordial black hole formation and generates a scalar-induced gravitational wave. These findings establish higher-order polynomial potentials as compelling frameworks and reconcile precision CMB measurements with multimessenger probes of early-universe physics.

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• Cosmology
• Evolution of the Universe
• Gravitational waves
• Inflation