Primordial Power Spectra, Low-$\ell$ CMB Anomaly, and Scale-Dependent Tensor-to-Scalar Ratio in Picard-Loop Quantum Cosmology

We investigate the evolution of scalar and tensor cosmological perturbations across the non-singularquantum bounce in Picard-Loop Quantum Cosmology (Picard-LQC). By solving the modifiedMukhanov-Sasaki equations with an explicit, C2-smooth spatial metric deformation function f(a), wecalculate the primordial scalar power spectrum Ps(k) and tensor spectrum Pt(k). We demonstratethat the quantum potential barrier at amin ≈ 0.5318 induces a natural infrared (IR) cutoff atkbounce ≈ 0.00055 Mpc−1. Mapping these modes to angular space yields a compelling fit to thePlanck 2018 low-ℓ CMB power suppression anomaly (ℓ < 30). Furthermore, we predict a scaledependent tensor-to-scalar ratio r(k) that decreases sharply from the standard inflationary benchmarkr ≈ 0.03 at small scales to r < 0.01 at large horizon scales, serving as a distinctive observationalsignature for upcoming B-mode polarization surveys. Full analytical derivations of perturbationvariables and vacuum boundary conditions are provided in the Appendix.