LQC inverse volume corrections inflation driven by fractional power law potentials in light of ACT observations

Abstract

Here, we investigate the observational viability of fractional power law inflationary potentials, $V(\varphi) \propto \varphi^n$ ($n=$ 1/3, 2/5, 2/3), within the effective framework of Loop Quantum Cosmology (LQC) incorporating inverse volume corrections. By employing LQC modifications to the background dynamics and cosmological perturbation equations in the semi-classical regime, we analytically derive the scalar spectral index $n_{\rm s}$ and the tensor-to-scalar ratio $r$. These theoretical predictions are confronted with the latest high precision joint observational constraints, including ACT DR6, Planck 2018, DESI BAO, and BICEP/Keck datasets (P-ACT-LB-BK18). While steeper classical power law models are in severe tension with modern data, our results demonstrate that the inclusion of LQC inverse volume effects induces a prominent negative shift in $n_{\rm s}$. Consequently, for specific viable ranges of the quantum geometric parameters ($\sigma$ and $\delta$), the theoretical predictions are translated horizontally across the $r-n_{\rm s}$ plane. This mechanism successfully steers classically disfavored models back into the tightly constrained 68\% and 95\% CLs, significantly improving their consistency with precision cosmological data.