Fractional power law inflationary potentials in loop quantum cosmology with inverse volume corrections in light of ACT observations

Abstract

Here, we investigate the observational viability of fractional power law inflationary potentials, $V(\phi )\propto {\phi }^n$ ($n=$ 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 $n_{\mathrm{s}}$ 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 $n_{\mathrm{s}}$. Consequently, for specific viable ranges of the quantum geometric parameters ($\sigma$ and $\delta$), the theoretical predictions are translated horizontally across the $r-n_{\mathrm{s}}$ 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.

21 pages, 5 figures, 2 tables