Exploring Statistical Isotropy in Planck Data Release 4: Angular Clustering and Cosmological Parameter Variations Across the Sky

The origin of small deviations from statistical isotropy in the Cosmic Microwave Background (CMB) - the so-called CMB anomalies - remains an open question in modern cosmology. In this work, we test statistical isotropy in Planck Data Release 4 (PR4) by estimating the temperature and $E$-mode power spectra across independent sky regions. We find that the directions with higher local bandpower amplitudes in intensity are clustered for multipoles between 200 and 2000 with clustering probabilities consistently below 1% for all these scales when compared to end-to-end (E2E) Planck simulations; notably, this range extends beyond that reported in Planck Data Release 3 (PR3). On the other hand, no significant clustering is observed in the polarization $E$-modes. In a complementary analysis, we search for dipolar variations in cosmological parameters fitted using the previously computed power spectra. When combining temperature and polarization power spectra, we identify a potential anomaly in the amplitude of the primordial power spectrum, $A_{s}$, with only 5 out of 600 simulations exhibiting a dipole amplitude as large as that observed in the data. Interestingly, the dipole direction aligns closely with the known hemispherical power asymmetry, suggesting a potential link between these anomalies. All other cosmological parameters remain consistent with $\Lambda\mathrm{CDM}$ expectations. Our findings highlight the need to further investigate these anomalies and understand their nature and potential implications for better understanding of the early Universe.