CMB Topology Reveals Significant Anisotropies
Our most successful cosmological model, Lambda Cold Dark Matter (ΛCDM), relies on the tenets set forth in the Cosmological Principle which states that at large scales, the universe is homogeneous and isotropic. These assumptions imply that no matter where you are, or in which direction you look, the universe will look about the same. The Cosmic Microwave Background is one of the many features ΛCDM has been able to predict.
As the early universe cooled, free electrons combined with protons to form neutral hydrogen in a process called recombination. This left behind a nearly transparent universe where photons could travel freely. The CMB is a snapshot of this moment, capturing the last interactions of these photons before they began their uninterrupted journey through space, remaining largely unaltered to this day. In 2018, the Planck collaboration released their final images of the CMB, granting us our best insights into the structure of the early universe, less than 400,000 years after the big bang.
However, this data has long been a point of contention, as it became clear that faint anisotropies could be observed within the CMB. Now, as study by Pratyush Pranav and Thomas Buchert demonstrate that certain anisotropies are quite significant. The duo leverage the final two releases of CMB data taken by the Planck satellite, PR3 and PR4.
The paper performs a topological analysis of the CMB data, utilising principles of persistent homology to quantify the intensity of temperature fluctuations within different regions of the sky. Homology as a study does this by quantifying the frequency of certain topological features, such as connected surfaces, loops and holes. Persistent homology extends these principles, by investigating how these same features change as we limit the surface to points that exceed differing threshold values. The results were subsequently compared to idealised temperature maps derived from ΛCDM models.
The team identified several statistically significant anomalies of unknown physical origin. Within the northern hemisphere, they observed notable deviations between the images at 1°, with the observed map featuring smaller, more fragmented structures than predicted by theory. Additionally, the northwestern quadrant of the CMB emerged as the most anomalous region. This is particularly noteworthy since it is one of the most directly accessible parts of the CMB, with less foreground contamination than other areas. As a result, it required minimal preprocessing. The localisation of these anomalies points to a preferred directionality, challenging the core assumption of statistical isotropy.
While these irregularities have been noted in previous studies, this work reveals that they may be more significant than previously thought. Furthermore, the detection of similar anomalies in multiple independent datasets strengthens the case for their existence. However, the authors remain cautious about fully attributing these anomalies to fundamental cosmological phenomena. They acknowledge that certain mathematical formalisms, such as normalisation, could influence the results, and that a more rigorous investigation into potential biases introduced during data preprocessing is required. To address this, they propose more advanced approaches that should mitigate or eliminate any such processing biases, ensuring a more robust confirmation of their findings.
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Journal Source: P. Pranav and T. Buchert, Homology reveals significant anisotropy in the cosmic microwave background, Astronomy and Astrophysics, Vol. 695, No. A35, (2025), DOI: https://doi.org/10.1051/0004-6361/202347761
Cover Image: ESA, Planck Collaboration