Polynomial Potential Inflation in the ACT Era: From CMB to Primordial Black Holes

Abstract

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 multi-messenger probes of early-universe physics.

25 pages, 6 figures, PRD accepted;