Inverse Reconstruction of the Primordial Spectrum from CMB Anomalies: Bayesian Evidence for Loop Quantum Cosmology

We present a novel inverse reconstruction of the primordial power spectrum P(k) using a constrained Bayesian framework applied to four statistically anomalous features of the CMB at large angular scales: power suppression, parity asymmetry, quadrupole-octopole alignment, and dipolar modulation. Without imposing any specific theoretical model, we infer the class of spectra most compatible with the Planck SMICA 2018 observations. We find that the reconstructed spectra systematically deviate from the predictions of standard inflationary ΛCDM, but align closely with forms previously derived from Loop Quantum Cosmology (LQC). This result provides a rare example of a model-agnostic inversion pointing toward a quantum gravitational origin of cosmological features. The implications for early- universe dynamics and falsifiability of inflationary paradigms are discussed.