Direct Observational Analysis of the Cosmic Microwave Background Angular Power Spectrum from Planck Data

This work presents a direct observational analysis of the Cosmic Microwave Background (CMB) angular power spectrum using the publicly available Planck SMICA full-sky temperature dataset. The CMB temperature field defined on the celestial sphere is decomposed into spherical harmonic modes and the corresponding angular power spectrum CℓC_ℓ is computed directly from the observational map. The procedure is entirely observational and avoids cosmological parameter fitting, theoretical priors, or model-dependent statistical reconstructions. The resulting spectrum reproduces the characteristic acoustic peak structure observed in Planck measurements while providing a transparent and reproducible computational framework. Particular attention is devoted to the large angular scale regime (ℓ<50 < 50ℓ<50), where the observed spectrum exhibits notable deviations from the smooth statistical expectations commonly associated with standard cosmological models. The analysis allows a direct inspection of these low-multipole features and highlights the importance of treating the observational dataset independently of cosmological parameter inference. The work demonstrates that a fully observational reconstruction of the CMB angular power spectrum can be obtained through explicit spherical harmonic decomposition of the Planck temperature map, providing a transparent reference framework for the investigation of large-scale CMB anisotropies.