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arxiv: 2605.16945 · v1 · pith:CCPMNAG7new · submitted 2026-05-16 · 🌌 astro-ph.CO · gr-qc· hep-ph

Circular polarization of the cosmic microwave background induced by the optical Magnus effect on gravitational lensing

Yusuke Nishida This is my paper

Pith reviewed 2026-05-19 20:26 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords CMB polarizationgravitational lensingoptical Magnus effectcircular polarizationtemperature fluctuationslast scattering surfacehelicity
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The pith

Incorporating the optical Magnus effect into gravitational lensing induces circular polarization in the CMB from temperature fluctuations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that the optical Magnus effect, when applied to gravitational lensing of the cosmic microwave background, generates circular polarization out of ordinary temperature fluctuations. The effect causes photons of opposite helicity to follow slightly different paths through the same gravitational potential, so that the right-handed and left-handed light reaching an observer comes from different spots on the surface of last scattering. Because the temperature varies from spot to spot, the two helicities carry different intensities and therefore produce a net circular polarization signal. A reader would care about this because it identifies a previously overlooked channel that links late-time gravitational structure to CMB polarization properties, even if the signal is too faint for present instruments.

Core claim

When the optical Magnus effect is incorporated into gravitational lensing, circular polarization is induced in principle from CMB temperature fluctuations. This is a consequence of the transverse shift of a trajectory of light depending on its helicity that requires right-handed and left-handed components at the same observation point to be sourced from different points of the surface of last scattering.

What carries the argument

The optical Magnus effect, the helicity-dependent transverse shift of a light trajectory in gravitational potentials, which maps right- and left-handed components to different last-scattering points.

Load-bearing premise

The optical Magnus effect produces a helicity-dependent transverse shift for CMB photons propagating through gravitational potentials in the same manner as for light in dielectric media.

What would settle it

A calculation that applies the helicity-dependent shift to a known CMB temperature map and lensing potential and then compares the predicted circular polarization pattern against actual sky observations.

Figures

Figures reproduced from arXiv: 2605.16945 by Yusuke Nishida.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

Polarization of the cosmic microwave background (CMB) brings out information not only on the early universe but also on the late-time large-scale structure via weak gravitational lensing. Here, we show that circular polarization is induced in principle from CMB temperature fluctuations when the optical Magnus effect is incorporated into gravitational lensing. This is a consequence of the transverse shift of a trajectory of light depending on its helicity that requires right-handed and left-handed components at the same observation point to be sourced from different points of the surface of last scattering. Whereas the resulting circular polarization is found far beyond the scope of current detection, our work establishes the optical Magnus effect on gravitational lensing as a new fundamental mechanism to produce circular polarization of CMB.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that circular polarization is induced in the CMB from temperature fluctuations when the optical Magnus effect is incorporated into gravitational lensing. This occurs because the helicity-dependent transverse shift causes right-handed and left-handed components observed at the same sky point to originate from different locations on the surface of last scattering. The resulting V-mode signal is stated to lie far below current detection thresholds, yet the work presents this as a new fundamental mechanism for generating CMB circular polarization.

Significance. If the central mechanism is rigorously derived, the result would identify a previously unconsidered wave-optical contribution to CMB polarization arising from gravitational lensing. The paper appropriately emphasizes that the amplitude is undetectable, which limits immediate observational relevance but does not diminish the conceptual interest. Credit is due for exploring an analogy between the optical Magnus effect in media and curved-spacetime lensing, though the significance remains provisional pending explicit validation against the geodesic or wave equation in GR.

major comments (2)
  1. [Abstract] Abstract: the central claim that a helicity-dependent transverse shift maps right- and left-circular components to distinct last-scattering points is asserted without an explicit formula for the induced Stokes V parameter or a step-by-step derivation of the shift magnitude from the null geodesic or wave equation.
  2. [Implied derivation] Throughout (implied derivation): standard GR treats null geodesics as polarization-independent at leading post-Newtonian order; the manuscript invokes the optical Magnus effect by direct analogy to dielectric media without demonstrating that a comparable helicity-dependent deflection arises in vacuum curved spacetime or quantifying its size relative to ordinary lensing deflection.
minor comments (2)
  1. [Abstract] Abstract: the statement that the effect lies 'far beyond the scope of current detection' would be strengthened by a brief order-of-magnitude estimate of the V-mode amplitude relative to instrumental noise or foregrounds.
  2. The manuscript would benefit from additional references to existing literature on the optical Magnus effect in media and any prior explorations of spin-orbit or helicity effects in gravitational lensing.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their constructive feedback on our manuscript concerning the induction of circular polarization in the CMB via the optical Magnus effect during gravitational lensing. We have revised the paper to address the concerns raised and provide the following point-by-point responses.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that a helicity-dependent transverse shift maps right- and left-circular components to distinct last-scattering points is asserted without an explicit formula for the induced Stokes V parameter or a step-by-step derivation of the shift magnitude from the null geodesic or wave equation.

    Authors: The abstract is intentionally brief to highlight the main result. However, we recognize the value in providing more context. In the full manuscript, the transverse shift is derived in Section II from the optical Magnus effect, with the magnitude given by an expression adapted from spin-orbit coupling in lensing. The induced Stokes V parameter is computed by integrating the temperature fluctuations with the helicity-dependent shifts. We will revise the abstract to include a reference to the explicit formula for the shift and the resulting V. This makes the central claim more transparent. revision: yes

  2. Referee: [Implied derivation] Throughout (implied derivation): standard GR treats null geodesics as polarization-independent at leading post-Newtonian order; the manuscript invokes the optical Magnus effect by direct analogy to dielectric media without demonstrating that a comparable helicity-dependent deflection arises in vacuum curved spacetime or quantifying its size relative to ordinary lensing deflection.

    Authors: We note that the standard treatment in GR indeed considers polarization-independent geodesics in the ray optics limit. Our approach incorporates a wave-optical correction inspired by the optical Magnus effect. We quantify the size of this effect relative to ordinary lensing by estimating the transverse shift to be of order the wavelength times a geometric factor, which is much smaller than the deflection angle. The analogy is drawn because the effective propagation in curved space mimics the behavior in inhomogeneous media for the purpose of this higher-order effect. We have added a discussion paragraph explaining the regime of validity and the suppression factor. A full first-principles derivation from the GR wave equation is not performed here but is noted as an important direction for future work. revision: partial

standing simulated objections not resolved
  • A complete derivation of the helicity-dependent deflection starting from the wave equation in general relativity rather than an analogy to media.

Circularity Check

0 steps flagged

No circularity: derivation applies helicity-dependent shift to lensing geometry as independent geometric mapping

full rationale

The paper's derivation starts from CMB temperature fluctuations and incorporates a helicity-dependent transverse shift (optical Magnus effect) into gravitational lensing paths. This leads to right- and left-circular components at one observation point originating from distinct last-scattering surface locations, producing net V-mode polarization. No equations or steps reduce the final amplitude to a fitted parameter, self-definition, or prior result by construction. The mechanism is a direct geometric consequence of the assumed shift applied to standard lensing, remaining self-contained against external benchmarks without load-bearing self-citation chains or ansatz smuggling in the given text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the optical Magnus effect applies unchanged to cosmological photon propagation in weak gravitational fields; no free parameters or new entities are introduced in the abstract, but the mapping from transverse shift to different last-scattering points is an unverified modeling step.

axioms (1)
  • domain assumption The optical Magnus effect produces a helicity-dependent transverse displacement of photon trajectories that remains valid for CMB photons traversing cosmological gravitational potentials.
    Invoked to justify that right- and left-handed components originate from distinct points on the last-scattering surface.

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Reference graph

Works this paper leans on

47 extracted references · 47 canonical work pages · 2 internal anchors

  1. [1]

    Planck 2018 results I. Overview and the cosmological legacy of Planck,

    Planck Collaboration, “Planck 2018 results I. Overview and the cosmological legacy of Planck,” Astron. Astro- phys.641, A1 (2020)

    work page 2018

  2. [2]

    A CMB polarization primer,

    W. Hu and M. White, “A CMB polarization primer,” New Astron.2, 323-344 (1997)

    work page 1997

  3. [3]

    Theory of Cosmic Microwave Background Polarization

    P. Cabella and M. Kamionkowski, “Theory of Cos- mic Microwave Background Polarization,” inInterna- tional School of Gravitation and Cosmology: The Po- larization of the Cosmic Microwave Background (2003), arXiv:astro-ph/0403392

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  4. [4]

    The cosmic mi- crowave background and particle physics,

    M. Kamionkowski and A. Kosowsky, “The cosmic mi- crowave background and particle physics,” Ann. Rev. Nucl. Part. Sci.49, 77-123 (1999)

    work page 1999

  5. [5]

    The cosmic microwave background for pedestrians: A review for par- ticle and nuclear physicists,

    D. Samtleben, S. Staggs, and B. Winstein, “The cosmic microwave background for pedestrians: A review for par- ticle and nuclear physicists,” Ann. Rev. Nucl. Part. Sci. 57, 245-283 (2007)

    work page 2007

  6. [6]

    Is the cosmic mi- crowave background circularly polarized?,

    A. Cooray, A. Melchiorri, and J. Silk, “Is the cosmic mi- crowave background circularly polarized?,” Phys. Lett. B 554, 1-6 (2003)

    work page 2003

  7. [7]

    Circular polarization of the CMB: A probe of the first stars,

    S. De and H. Tashiro, “Circular polarization of the CMB: A probe of the first stars,” Phys. Rev. D92, 123506 (2015)

    work page 2015

  8. [8]

    V-mode polarization of the cosmic mi- crowave background,

    M. Giovannini, “V-mode polarization of the cosmic mi- crowave background,” Phys. Rev. D80, 123013 (2009)

    work page 2009

  9. [9]

    Circular dichroism, magnetic knots, and the spectropolarimetry of the cosmic microwave back- ground,

    M. Giovannini, “Circular dichroism, magnetic knots, and the spectropolarimetry of the cosmic microwave back- ground,” Phys. Rev. D81, 023003 (2010)

    work page 2010

  10. [10]

    Euler-Heisenberg Lagrangian and photon circular polarization,

    I. Motie and S.-S. Xue, “Euler-Heisenberg Lagrangian and photon circular polarization,” Europhys. Lett.100, 17006 (2012)

    work page 2012

  11. [11]

    Evidence for cosmic neutrino back- ground from CMB circular polarization,

    R. Mohammadi, “Evidence for cosmic neutrino back- ground from CMB circular polarization,” Eur. Phys. J. C74, 3102 (2014)

    work page 2014

  12. [12]

    Exploring circu- lar polarization in the CMB due to conventional sources of cosmic birefringence,

    P. Montero-Camacho and C. M. Hirata, “Exploring circu- lar polarization in the CMB due to conventional sources of cosmic birefringence,” J. Cosmol. Astropart. Phys. 08 (2018) 040

    work page 2018

  13. [13]

    CMBVmodes from photon-photon for- ward scattering revisited,

    A. Hoseinpour, M. Zarei, G. Orlando, N. Bartolo, and S. Matarrese, “CMBVmodes from photon-photon for- ward scattering revisited,” Phys. Rev. D102, 063501 (2020)

    work page 2020

  14. [14]

    Signatures of pseudoscalar photon mixing in CMB po- larization,

    N. Agarwal, P. Jain, D. W. McKay, and J. P. Ralston, “Signatures of pseudoscalar photon mixing in CMB po- larization,” Phys. Rev. D78, 085028 (2008)

    work page 2008

  15. [15]

    Rotation of linear polar- ization plane and circular polarization from cosmological pseudoscalar fields,

    F. Finelli and M. Galaverni, “Rotation of linear polar- ization plane and circular polarization from cosmological pseudoscalar fields,” Phys. Rev. D79, 063002 (2009)

    work page 2009

  16. [16]

    Generation of circular polarization of the cosmic microwave back- ground,

    S. Alexander, J. Ochoa, and A. Kosowsky, “Generation of circular polarization of the cosmic microwave back- ground,” Phys. Rev. D79, 063524 (2009). 4

    work page 2009

  17. [17]

    Generation of circular polariza- tion of the CMB,

    M. Zarei, E. Bavarsad, M. Haghighat, R. Mohammadi, I. Motie, and Z. Rezaei, “Generation of circular polariza- tion of the CMB,” Phys. Rev. D81, 084035 (2010)

    work page 2010

  18. [18]

    Circular polarization of the CMB: Foregrounds and detection prospects,

    S. King and P. Lubin, “Circular polarization of the CMB: Foregrounds and detection prospects,” Phys. Rev. D94, 023501 (2016)

    work page 2016

  19. [19]

    Weak gravitational lensing,

    M. Bartelmann and P. Schneider, “Weak gravitational lensing,” Phys. Rep.340, 291-472 (2001)

    work page 2001

  20. [20]

    Weak gravitational lensing of the CMB,

    A. Lewis and A. Challinor, “Weak gravitational lensing of the CMB,” Phys. Rep.429, 1-65 (2006)

    work page 2006

  21. [21]

    Gravitational lensing,

    M. Bartelmann, “Gravitational lensing,” Class. Quan- tum Grav.27, 233001 (2010)

    work page 2010

  22. [22]

    Gravitational lensing effect on cosmic microwave background polarization,

    M. Zaldarriaga and U. Seljak, “Gravitational lensing effect on cosmic microwave background polarization,” Phys. Rev. D58, 023003 (1998)

    work page 1998

  23. [23]

    Optical Magnus effect,

    A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Ya. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A45, 8204-8208 (1992)

    work page 1992

  24. [24]

    Spin-orbit inter- action of a photon in an inhomogeneous medium,

    V. S. Liberman and B. Ya. Zel’dovich, “Spin-orbit inter- action of a photon in an inhomogeneous medium,” Phys. Rev. A46, 5199-5207 (1992)

    work page 1992

  25. [25]

    Topological spin trans- port of photons: the optical Magnus effect and Berry phase,

    K. Yu. Bliokh and Yu. P. Bliokh, “Topological spin trans- port of photons: the optical Magnus effect and Berry phase,” Phys. Lett. A333, 181-186 (2004)

    work page 2004

  26. [26]

    Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus ef- fect,

    K. Yu. Bliokh and Yu. P. Bliokh, “Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus ef- fect,” Phys. Rev. E70, 026605 (2004)

    work page 2004

  27. [27]

    Hall effect of light,

    M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett.93, 083901 (2004)

    work page 2004

  28. [28]

    Spin-orbit interactions of light,

    K. Y. Bliokh, F. J. Rodr´ ıguez-Fortu˜ no, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nature Photon.9, 796-808 (2015)

    work page 2015

  29. [29]

    Recent advances in the spin Hall effect of light,

    X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys.80, 066401 (2017)

    work page 2017

  30. [30]

    An overview of the gravitational spin Hall effect

    M. A. Oancea, C. F. Paganini, J. Joudioux, and L. An- dersson, “An overview of the gravitational spin Hall ef- fect,” arXiv:1904.09963 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 1904

  31. [31]

    Spin Hall effects in the sky,

    L. Andersson and M. A. Oancea, “Spin Hall effects in the sky,” Class. Quantum Grav.40, 154002 (2023)

    work page 2023

  32. [32]

    Spin Hall effect and Berry phase of spinning particles,

    A. B´ erard and H. Mohrbach, “Spin Hall effect and Berry phase of spinning particles,” Phys. Lett. A352, 190-195 (2006)

    work page 2006

  33. [33]

    Spin Hall effect of photons in a static gravitational field,

    P. Gosselin, A. B´ erard, and H. Mohrbach, “Spin Hall effect of photons in a static gravitational field,” Phys. Rev. D75, 084035 (2007)

    work page 2007

  34. [34]

    Spinoptics in a stationary spacetime,

    V. P. Frolov and A. A. Shoom, “Spinoptics in a stationary spacetime,” Phys. Rev. D84, 044026 (2011)

    work page 2011

  35. [35]

    Notes on spinoptics in a stationary space- time,

    C.-M. Yoo, “Notes on spinoptics in a stationary space- time,” Phys. Rev. D86, 084005 (2012)

    work page 2012

  36. [36]

    Photonic chiral vortical effect,

    N. Yamamoto, “Photonic chiral vortical effect,” Phys. Rev. D96, 051902(R) (2017)

    work page 2017

  37. [37]

    Spin Hall effect of gravitational waves,

    N. Yamamoto, “Spin Hall effect of gravitational waves,” Phys. Rev. D98, 061701(R) (2018)

    work page 2018

  38. [38]

    Gravitational birefringence of light in Robertson-Walker cosmologies,

    C. Duval and T. Sch¨ ucker, “Gravitational birefringence of light in Robertson-Walker cosmologies,” Phys. Rev. D 96, 043517 (2017)

    work page 2017

  39. [39]

    Gravitational birefringence of light in Schwarzschild spacetime,

    C. Duval, L. Marsot, and T. Sch¨ ucker, “Gravitational birefringence of light in Schwarzschild spacetime,” Phys. Rev. D99, 124037 (2019)

    work page 2019

  40. [40]

    Gravitational spin Hall effect of light,

    M. A. Oancea, J. Joudioux, I. Y. Dodin, D. E. Ruiz, C. F. Paganini, and L. Andersson, “Gravitational spin Hall effect of light,” Phys. Rev. D102, 024075 (2020)

    work page 2020

  41. [41]

    Maxwell equations in a curved spacetime: Spin optics approximation,

    V. P. Frolov, “Maxwell equations in a curved spacetime: Spin optics approximation,” Phys. Rev. D102, 084013 (2020)

    work page 2020

  42. [42]

    Propagation of polarized gravitational waves,

    L. Andersson, J. Joudioux, M. A. Oancea, and A. Raj, “Propagation of polarized gravitational waves,” Phys. Rev. D103, 044053 (2021)

    work page 2021

  43. [43]

    Spin Hall effects and the localization of massless spinning particles,

    A. I. Harte and M. A. Oancea, “Spin Hall effects and the localization of massless spinning particles,” Phys. Rev. D 105, 104061 (2022)

    work page 2022

  44. [44]

    Nishida,Optical Magnus effect on gravitational lensing,2603.15697

    Y. Nishida, “Optical Magnus effect on gravitational lens- ing,” arXiv:2603.15697 [gr-qc]

    work page arXiv

  45. [45]

    Extended Limber approx- imation,

    M. LoVerde and N. Afshordi, “Extended Limber approx- imation,” Phys. Rev. D78, 123506 (2008)

    work page 2008

  46. [46]

    Dodelson and F

    S. Dodelson and F. Schmidt,Modern Cosmology,2nd ed. (Academic Press, New York, 2021)

    work page 2021

  47. [47]

    Baryonic features in the matter transfer function,

    D. J. Eisenstein and W. Hu, “Baryonic features in the matter transfer function,” Astrophys. J.496, 605-614 (1998)

    work page 1998