TORONTO, ON, October 10, 2026 —
One half of the microwave sky is slightly brighter in its fluctuations than the other. A new study from the Institute derives the direction and the size of this lopsidedness from a single assumption about the universe as a whole: it is closed, and it counter-rotates. The study states in advance how the effect should weaken on smaller angular scales. It then tests that statement on the four Planck microwave maps. The maps follow the predicted curve, and they rule out the simplest alternative.
Video overview:
The preprint:
Kriger, B. (2026, October). What counter-rotation adds to elliptic space: A hemispherical dipole perpendicular to the spin-chirality axis, an invisible topology, and two corrections. IIIR Cosmology and Theoretical Physics. https://doi.org/10.13140/RG.2.2.33438.09286
The problem, restated.
For twenty years, maps from WMAP and then Planck have shown a hemispherical power asymmetry. Temperature fluctuations are about seven to nine percent stronger in one half of the sky than in the other. Standard cosmology treats the sky as statistically the same in every direction and has no reason for this. Most proposed explanations add a modulating field with its own direction, strength and scale law. None of them connects the asymmetry to anything else in the sky.
One construction, one invariant.
The Institute’s research programme places a global double counter-rotation on elliptic space, the closed space in which opposite points are identified. Two rotations in perpendicular planes carry opposite angular momenta, so the total is zero. Using the eigenmode framework recently published by the COMPACT collaboration for this family of spaces, the study shows that the whole configuration reduces to a single mode of the lowest nontrivial degree. On the sphere from which the microwave light reaches us, that mode produces a dipole, a hemispherical asymmetry, and nothing at finer angular structure.
A right angle between two anomalies.
Every rotational quantity of the configuration lies in one surface, the Clifford torus through the observer. The asymmetry it produces points along the normal to that surface. The microwave asymmetry must therefore be perpendicular to the axis along which the programme expects galaxies to show a preferred direction of spin. Both axes have been measured independently. The measured angle between them is 79 degrees in WMAP, 89.7 degrees in a recent multi-map average, and 88 degrees in the Planck maps analysed here.
The size and the slope from the initial state.
The programme starts the universe as a compact counter-rotating state whose rim moves at the speed of light, so that proper time nearly stands still. Each fluctuation mode remembers the rotation until a sound wave crosses it, and this fixes how the asymmetry weakens with angular scale. Only one free parameter remains: the observer’s position in the rotating space. Fixing it with the measured amplitude at multipole 10 gives a slope of −0.29 across multipoles 6 to 30. The measured value is −0.31 ± 0.16.
A prediction written down first.
The first version of the paper also stated what the asymmetry should be on scales where it had not been fitted: about 0.038 at multipole 60, 0.024 at 100 and 0.011 at 200. Before any map was opened, the predicted values for four bands were written to a file and its cryptographic fingerprint was recorded. The test was then run on the SMICA, Commander, NILC and SEVEM maps of the Planck 2018 release and calibrated against 1,400 simulated skies.
What the maps show.
- In all four maps the asymmetry weakens from multipole 30 to 400 along the predicted curve, with χ² below 1 for four bands and nothing adjusted.
- A straight extension of the measured power law is ruled out, with χ² ≈ 32 for the same four bands.
- An isotropic sky would produce an equally strong preference for the predicted curve in fewer than one simulation in a hundred (p = 0.008).
- The result survives a much more conservative sky mask, and the four maps agree closely with one another.
“We wrote the curve down, published it, fingerprinted the numbers, and only then opened the maps,” said Boris Kriger, Lead Investigator. “They could have shown the asymmetry running on as a power law, or vanishing early. They did neither. That is the kind of agreement a model has to earn, not one it can be fitted into.”
What would falsify this.
- An asymmetry axis that is not perpendicular to a confirmed galaxy-spin chirality axis.
- An asymmetry above multipole 400 well above the predicted values, which fall to about 0.001 near multipole 1000.
- A spatial curvature measured as flat in a way that survives the question of how the sound horizon is calibrated. At flat curvature the predicted amplitude cannot be reached.
What is not claimed.
The agreement holds at the closed curvature Ω_K = −0.044 preferred by the Planck spectra alone, which the programme adopted in March 2026. It does not hold at the flat curvature preferred when baryon acoustic oscillations are added, and the paper says so. Weakening of the asymmetry on small scales is already known; what is new is that a curve computed in advance fits the shape of that weakening. The preference over an isotropic sky is about 2.4 standard deviations. The programme’s chirality axis coincides with the direction of the microwave dipole, so the perpendicularity test carries weight only to the extent that the dipole is not purely due to our own motion. The paper also withdraws two of the programme’s earlier claims: that elliptic space suppresses the quadrupole, and that its polarization signature is absent from the diagonal.
An invitation.
Every number in the paper is produced by code printed in its appendix. The study specifies a covariance for the full likelihood analysis, and it has been offered to the COMPACT collaboration. The Institute invites independent groups to repeat the Planck test with the official end-to-end simulations and to extend it to multipole 1000. Contact: boriskriger@interdisciplinary-institute.org
Full αLGQV programme:
https://interdisciplinary-research.institute/cosmology-and-theoretical-physics/
Reception and correspondence
Boris Kriger
Lead Investigator
ORCID: https://orcid.org/0009-0001-0034-2903
Institute of Integrative and Interdisciplinary Research, Toronto
+1 437-552-8807
boriskriger@interdisciplinary-institute.org
interdisciplinary-research.institute
About the Institute
The Institute of Integrative and Interdisciplinary Research is a Toronto-based organization that addresses complex problems by combining rigorous formal methods with work across disciplines, treating interdisciplinarity as a methodological requirement and connecting specialized fields into coherent theoretical frameworks.
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