Cosmic Topology Hints vs Circle-Search Nulls

The large-angle CMB looks the way a finite or multiply connected universe should look: power suppressed at the largest scales, the quadrupole at a quarter of its expected value, multipoles aligned along preferred axes, and power distributed asymmetrically between hemispheres. These are exactly the signatures cosmic topology produces, which is why the COMPACT collaboration argued in Physical Review Letters (2024, arXiv:2210.11426) that the anomalies may carry detectable topological information and that the observational window remains wide open. Yet the direct searches say no: matched-circle analyses of WMAP and Planck, which would find pairs of identical circles on the last-scattering surface if light had wrapped the universe, are null, and Planck's Bayesian likelihood searches exclude the best-studied flat and spherical topologies out to scales comparable to the observable diameter.

That combination puts ΛCDM in an awkward spot of its own making. The model assumes trivial topology, infinite simply connected flat space, as a default with no mechanism behind it; inflation generically predicts the observable patch is a vanishing fraction of any topological identification scale, making hints undetectable in principle. So the model can neither explain why the large-angle sky carries topology-like signatures (it must call them flukes of cosmic variance) nor accommodate actual topology if the hints are real (its own initial-conditions theory says we should never see it). The data are self-consistently strange: every indirect statistic whispers finite while every direct test shouts unbounded.

The standing is active again after a decade dormant: COMPACT has shown that most orientable topologies are not yet excluded, that anomaly statistics contain unexploited discriminating power, and that LiteBIRD-class polarization plus future 21-cm data could detect identifications well beyond the circle-search horizon. Either the hints sharpen into the discovery of cosmic topology, or the anomalies need an explanation that mimics finiteness without any actual identification of points.

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