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

This paper presents a direct observational analysis of the Cosmic Microwave Background (CMB) angular power spectrum using the publicly available Planck SMICA full-sky temperature map. The CMB temperature field is decomposed into spherical harmonic modes and the angular power spectrum Cℓ is computed directly from the observational dataset without introducing cosmological parameter fitting or model-dependent assumptions. The resulting spectrum reproduces the main acoustic peak structure observed in the Planck measurements while allowing a transparent inspection of large-scale anisotropies. Particular attention is devoted to the low multipole region (ℓ<50), where the observed spectrum exhibits notable deviations from the smooth statistical behaviour often assumed in standard cosmological models. The work highlights the importance of direct observational reconstruction of the CMB power spectrum as a complementary approach to model-driven cosmological inference.