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REVIEW 3 major objections 4 minor 83 references

This paper argues that cosmic birefringence can directly test Swampland conjectures, because its angular pattern separates ultralight axions from thin domain walls.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-01 09:40 UTC pith:47C2FXX7

load-bearing objection A useful map of the birefringence–Swampland interface, but the isotropic/anisotropic discriminator is asserted, not derived, and may not survive contact with actual perturbation amplitudes. the 3 major comments →

arxiv 2607.27318 v1 pith:47C2FXX7 submitted 2026-07-29 hep-th astro-ph.COgr-qchep-ph

Wading the String Bog: CMB Birefringence in the Swampland

Guido D'Amico , Nemanja Kaloper , Alexander Westphal This is my paper
classification hep-th astro-ph.COgr-qchep-ph
keywords cosmic birefringenceCMB polarizationSwampland conjecturesweak gravity conjectureultralight axionaxionic domain wallsChern-Simons couplingdark energy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Cosmic birefringence—a tiny rotation of CMB polarization, hinted at about 0.3 degrees—is usually explained by ultralight axion fields that roll slowly across cosmological distances. The paper argues that this explanation conflicts with the Weak Gravity Conjecture: making the rotation large enough needs very small axion masses and Planckian field excursions, while the conjectured bound on axion mass and decay constant pushes in the opposite direction. The paper's alternative is that the same rotation can be produced by CMB photons crossing thin axionic domain walls, with no propagating ultralight field at all, and that this alternative is Swampland-compatible. The two mechanisms predict opposite angular patterns—wall-induced birefringence is exactly isotropic, ultralight-induced birefringence generically anisotropic—so measuring birefringence anisotropies can decide between them.

Core claim

Within the Swampland framework, the paper's central claim is that invoking an ultralight axion to explain the suggested CMB polarization rotation ϑ ∼ 10^-3 radians is in genuine tension with the magnetic Weak Gravity Conjecture bound Λ³_QCD ≲ m f M_Pl. For decay constants f ∼ 10^11–10^16 GeV this bound forces m ≳ 10^-28–10^-23 eV, right next to the mass range m ≲ 10^-28 eV that the birefringence signal requires. The same rotation, however, can be produced by vacuum interfaces: thin axionic domain walls with residual electromagnetic Chern–Simons couplings twist photon polarizations by a discrete Pancharatnam phase. Under minimal assumptions, the accumulated twist along any line of sight equal

What carries the argument

The central object is the parity-violating axion–photon Chern–Simons coupling g φ F∧F, whose two regimes carry the argument. In the adiabatic regime of a slow-rolling ultralight axion, the polarization rotation is ϑ = (1/2) g Δφ, with Δφ potentially trans-Planckian; the magnetic WGC bound Λ³_QCD ≲ m f M_Pl then imports the conflicting lower bound on m. In the non-adiabatic regime of a thin wall, the coupling acts as a discrete jump Δθ δ(z), and the exact (1+1)-dimensional scattering solution yields helicity phases e^{∓iϑ} and a topological angle ϑ(n̂) = θ_final − θ_initial. The argument also leans on the two-step Sakharov-like picture—Thomson scattering first creates linear polarization, a p

Load-bearing premise

The whole claimed tension rests on the conjectural magnetic Weak Gravity Conjecture bound applied to the QCD-axion sector, Λ³_QCD ≲ m f M_Pl, together with the assumption that every axion inheriting the electromagnetic Chern–Simons coupling must obey the resulting lower mass bound m ≳ Λ³_QCD/(M_Pl f); if this inequality is weaker, inapplicable to mixed or Clockwork sectors, or carries different numerical factors, the ultralight-axion explanation is not in conflict with Swampl

What would settle it

A high-precision CMB polarization map that detects a direction-dependent rotation angle (anisotropic birefringence) would falsify the exact-isotropy prediction of the thin-wall mechanism and favour the ultralight-axion explanation; a null anisotropy search at the expected sensitivity would falsify the minimal anisotropic-ultralight explanation. Alternatively, a first-principles string construction with an ultralight axion of m ≲ 10^-33 eV and f ≳ M_Pl coupled to F F̃ would violate the magnetic WGC bound if that bound is correct, settling the tension claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A confirmed anisotropic birefringence pattern would point to cosmological ultralight fields with large field excursions, and would put pressure on Swampland expectations.
  • A confirmed isotropic signal would favour thin axionic domain walls (vacuum interfaces) as the source, consistent with Weak Gravity Conjecture constraints.
  • The two scenarios can be separated by existing and upcoming CMB polarization experiments measuring anisotropy, and by comparing CMB rotation with radio-galaxy rotation; a positive CMB signal with a null radio-galaxy signal favours early walls.
  • Wall-induced birefringence is exactly isotropic and independent of redshift and frequency below the cutoff; any tomographic or frequency dependence of the rotation would instead indicate a rolling ultralight field.
  • If birefringence is real, its observed pattern becomes a rare experimental probe of Planck-scale physics and quantum-gravity constraints.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Inference: an isotropic result would not prove the Swampland program, but it would remove the sharpest phenomenological conflict with it; the ultralight-axion explanation would remain viable only in heavily fine-tuned corners where fluctuations and anisotropies are suppressed.
  • Inference: the paper's trick of spreading the electromagnetic coupling across a Clockwork chain before generating the mass hierarchy suggests a concrete model-building test—search for axion landscapes in which the photon coupling is 'flavour-democratic' rather than localized, which would make ultralight birefringence easier to realize.
  • Inference: the Sakharov-like two-step logic implies the same vacuum-interface twist should act on any polarized source behind the walls, not just the CMB; comparing rotation across source redshifts and frequencies is a natural extension of the paper's central dichotomy.
  • Inference: if anisotropies are detected, the next quantitative step is to compute the magnetic WGC bound with precise numerical coefficients and apply it to the specific multi-axion construction here—this would either sharpen the claimed tension or dissolve it, deciding whether the Swampland clash is real.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper argues that a future detection of cosmic birefringence could provide a direct experimental test of Swampland conjectures. It reviews the standard adiabatic ultralight-axion mechanism, showing that an observed rotation ϑ ∼ 10^-3 would require axion masses m ≲ 10^-28 eV and Planckian field excursions. It then constructs a Clockwork-like multi-axion see-saw in which the electromagnetic Chern-Simons coupling is shared before mass diagonalization, obtaining g_ultra ∼ 10^-19–10^-24 GeV^-1 and rotations in the hinted range. Section 6 applies electric and magnetic WGC bounds and argues for a genuine but order-of-magnitude tension between ultralight birefringence and Swampland expectations. Section 7 reviews the alternative thin-domain-wall / vacuum-interface mechanism, exactly solves photon propagation through a θ-jump, and derives a Pancharatnam phase. The central claim is that wall-induced birefringence is exactly isotropic while bulk ultralight fields necessarily produce anisotropic birefringence, so anisotropy measurements by POLARBEAR, Simons Observatory, and LiteBIRD can discriminate the two mechanisms and thereby test Swampland ideas.

Significance. If the anisotropy discriminator were quantitatively correct, the paper would connect quantum-gravity conjectures to near-future CMB polarization data in a concrete and falsifiable way. The exact thin-wall transfer matrix in Eqs. (34)–(39) is a clean derivation, and the observation that wall-induced rotation depends only on the initial and final vacua (Eqs. (41)–(42)) is insightful. The paper is also honest about the uncertainties in the WGC bounds and about the model-dependence of the Clockwork coupling-sharing construction. However, the key phenomenological dichotomy is not established: for a homogeneous rolling ultralight field, the leading-order birefringence is isotropic, and the paper provides no estimate of the perturbation-level anisotropy. This weakens the claimed experimental test. The paper remains useful as a synthesis and as a map of the available parameter space, but its headline conclusion needs substantial qualification or a genuine calculation.

major comments (3)
  1. [Sec. 7, final paragraph; Eq. (24)] The central 'mutually exclusive' discriminator is not supported. Eq. (24), ϑ = g Δϕ/2, is an integral along the line of sight of a homogeneous rolling field, so at zeroth order it is independent of n̂. The statement that 'bulk ultralight fields necessarily produce anisotropic birefringence' is therefore too strong; direction dependence enters only through perturbations δϕ and metric fluctuations. The paper gives no estimate of δϑ/ϑ̄. For a quintessence field with Planckian excursions and inflationary fluctuations δϕ ∼ H_infl/(2π), one typically obtains δϑ/ϑ̄ ≲ 10^-6, far below the sensitivities of the experiments quoted. The Sec. 1 assertion of 'O(1) factors from direction to direction' is likewise unquantified. Since both mechanisms predict an isotropic leading-order signal, an anisotropy search alone cannot discriminate them; the authors should either compute the perturbation-level ani
  2. [Sec. 6, Eqs. (30)–(32)] The claimed 'genuine tension' with the Swampland rests on the magnetic WGC bound Λ_QCD^3 ≲ m f M_Pl applied to the QCD axion and to all fields that inherit its Chern-Simons coupling. The authors explicitly acknowledge that numerical coefficients are not reproduced. For f ∼ 10^16 GeV the bound gives m ≳ 10^-28 eV, which sits exactly at the Eq. (4) requirement, so an O(1) coefficient can remove the tension; for f ∼ 10^11 GeV the tension is stronger, but the applicability of the bound to the see-saw/Clockwork eigenstate is not demonstrated. This point should be presented as an order-of-magnitude motivation rather than a component of an exclusion claim, and the paper should state explicitly what would falsify the application to the mixed axion sector.
  3. [Sec. 7, Eq. (42) and Sec. 8, Figs. 2–3] The wall-induced isotropy result depends on the assumptions that all last-scattering photons share the same initial vacuum and all observers share the same final vacuum, as the paper notes. This is a plausible boundary condition in the DED scenario, but it is not automatic. The numerical spectra in Figs. 2 and 3 are presented without specifying the Boltzmann solver, input cosmological parameters, or the normalization of ϑ, making the forecasted discrimination difficult to reproduce. Please provide these details or clearly label the figures as illustrative sketches.
minor comments (4)
  1. [Abstract and Sec. 9] The abstract says confirming ultralight-axion birefringence 'could spell problems' for the Swampland, while the body carefully uses 'tension' and disclaims an exclusion. Please align the abstract with the more cautious statements in the text.
  2. [Sec. 2, Eq. (3)] The Riemann-Lebesgue argument leading to Eq. (3) is sketched very briefly. A few more intermediate steps or a reference to a detailed derivation would help the reader verify the dependence on m t_i and the claimed suppression.
  3. [Sec. 5, Eq. (26)] The observational hint ϑ ≃ 0.3 degrees is quoted without error bars or a distinction between central value and upper limit. Please cite the specific measurement and state the uncertainty, since the later parameter choices are calibrated to this number.
  4. [Throughout] There are repeated typos such as 'difficulties' and 'sufficiently', and Eq. (1) has a line break that obscures the normalization g/4. A careful proofreading pass is needed.

Circularity Check

2 steps flagged

Two load-bearing self-citation chains (magnetic WGC bound and the domain-wall/DED mechanism) support the central claims, though the core derivations are re-derived and no fitted quantity is renamed as a prediction.

specific steps
  1. self citation load bearing [Sec. 6, around Eqs. (30)-(31)]
    "A more practical approach is to use the magnetic version of WGC, which was discussed in [ 6,64]. There, it was shown that ... The WGC bound relates the domain wall tension and coupling to the Planck scale, T < gM Pl, and since for a monodromized axion g ∼ mf , this yields the bound Λ3 ∼ mf MPl [64]"

    The quantitative bound producing the claimed 'genuine tension' between Swampland constraints and ultralight-axion birefringence is not derived in this paper; it is imported from [64], whose author list includes Westphal, a co-author of the present paper. The paper itself concedes 'we did not reproduce carefully all required numerical coefficients,' so the load-bearing inequality Λ^3_QCD ≲ m f M_Pl is an unverified self-citation. If that bound is weakened or inapplicable, the stated tension with Eq. (4) evaporates; the argument therefore rests on the authors' prior work rather than on an independently established result.

  2. self citation load bearing [Sec. 7 'Land Ho!', Eqs. (33)-(42), and Sec. 9]
    "Interestingly, in the light of the very recent work [ 29–31] the answer is in the negative. ... The precise and detailed analysis of this process is given in [ 29–31]. We merely summarize its principal features here."

    The alternative resolution that avoids the Swampland tension is anchored in Kaloper's own recent papers [29-31] and the Discretely Evanescent Dark Energy proposal [16], all authored or co-authored by the present paper's co-author N. Kaloper. Although the paper re-derives some of the wall-crossing algebra and the endpoint formula Eq. (42), the key exact solution is presented as 'the exact solution [31]' and the late-time wall boundary conditions (same initial and final vacuum) are taken from [16]. Thus the central claim that domain walls provide an isotropic, Swampland-compatible explanation is not independently established in this paper; it is carried by a chain of self-citations.

full rationale

The paper is not circular in the narrow sense of fitting a parameter and then calling the fit a prediction: the adiabatic rotation formula ϑ = ½ g Δϕ (Eq. 24) and the thin-wall endpoint formula ϑ(n̂) = θ_final − θ_initial (Eq. 42) are genuine consequences of the stated wave equations and boundary conditions, and the WGC input is partly anchored in external references [6] and recent work [65,66]. No step reduces to its input by construction. However, two load-bearing elements are imported from the authors' own prior work: (i) the magnetic WGC bound Eq. (30)-(31), taken from [64] with Westphal as a co-author and explicitly not re-derived with careful coefficients, and (ii) the entire wall/DED mechanism from [16,29-31], all by Kaloper. These citations are central to the paper's two headline conclusions: that ultralight axions face a genuine Swampland tension and that domain walls evade it. The assertion that 'bulk ultralight fields necessarily produce anisotropic birefringence' is stated without a calculation and is questionable for a homogeneous quintessence background, but that is a correctness risk rather than a circularity. Weighing everything, the central derivations have independent content, so a score of 4 rather than 6 or higher is appropriate.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 1 invented entities

The central tension claim rests on one conjectural quantum-gravity inequality plus a specific mixing/Clockwork construction with several hand-picked scales. The wall alternative rests on a self-cited model (DED) whose internal parameters (Cγ, dark sector scales) are chosen to match the observed hint. The paper's own honest hedging is reflected in these entries.

free parameters (5)
  • Clockwork gear ratio q = 10
    Chosen by hand in Eq (15) to rapidly generate the mass hierarchy; no derivation from an underlying UV model.
  • Clockwork chain length N = ~18
    Set by Eq (18) so that m_ultra/m ~ 10^-18 with q=10, i.e. tuned to reach the target ultralight mass 10^-33 eV.
  • Intermediate dark-sector mass scale m = ~10^-15 eV
    Benchmark chosen 'not too far from the QCD axion mass range' in §4; the coupling and mass-hierarchy estimates scale with it.
  • Wall Chern-Simons coefficient Cγ = O(1)
    In Eq (40), Δθ = 10^-3 Cγ; setting Cγ ~ O(1) makes the wall prediction match the observed hint ϑ ~ 10^-3.
  • QCD axion mass/coupling benchmarks m_QCD, g_ϕγγ = 10^-10 eV, 10^-13 GeV^-1
    Used in §4-5 to produce g_ultra ~ few × 10^-19 GeV^-1; values are near current bounds but not derived.
axioms (4)
  • domain assumption The (magnetic) Weak Gravity Conjecture applies to axions and domain walls: Λ^3 ≲ m f M_Pl.
    Section 6, Eq (30); the tension is computed using this conjectural inequality from [6,64]. If the conjecture is false or weaker, the central tension fails. The paper explicitly notes ongoing debate about WGC strength.
  • domain assumption DED dark confining sector with strong scale ~10^-3 eV and membrane nucleation rate Γ ~ H0^4 produces percolating thin walls after recombination.
    Section 7, from [16]; provides the 'natural answer' for why CMB photons cross walls late. This is a self-cited model assumption.
  • ad hoc to paper The QCD axion mixes with the ultralight/dark axion sector via kinetic and mass mixings, and the electromagnetic coupling vector is distributed democratically across N≈18 Clockwork sites.
    Eqs (11)-(17); the viability of g_ultra ~ g_ϕγγ m/(√N m_QCD) depends on coupling redistribution before Clockwork hierarchy generation, which the paper admits is not guaranteed by first-principles constructions.
  • domain assumption No cosmic strings; the θ-vacuum map is single-valued so dθ is exact and wall birefringence is isotropic.
    Section 7, before Eq (41): 'because θ labels vacua and no strings are present... dθ is globally exact'. If strings exist or inflation does not homogenize the initial vacuum, anisotropy can arise, breaking the sharp discriminator.
invented entities (1)
  • Thin axionic domain walls / vacuum interfaces bearing residual θF F~ couplings independent evidence
    purpose: Produce CMB birefringence without propagating ultralight axions, avoiding Planckian excursions and WGC tension.
    Introduced in refs [29-31,16] (co-authored by Kaloper) and summarized in §7. The paper gives falsifiable handles: exactly isotropic rotation, frequency-independent below cutoff, step-function redshift imprint, and null rotation for radio galaxies. No direct observational evidence yet.

pith-pipeline@v1.3.0-daily-deepseek · 24435 in / 15101 out tokens · 120858 ms · 2026-08-01T09:40:10.363670+00:00 · methodology

0 comments
read the original abstract

We point out that observations of cosmic birefringence may provide direct experimental tests of Swampland conjectures. Ultralight scalar field birefringence mechanisms are constrained by Weak Gravity Conjecture, limiting their parameter space. Conversely, confirming that CMB birefringence is caused by ultralight scalars could spell problems for the Swampland framework. Resolving these difficulties without a revision of Swampland ideology points toward thin axionic domain walls, which can explain birefringence without propagating ultralight degrees of freedom. Importantly these conflicting scenarios for cosmic birefringence could be experimentally distinguished by a search for, or exclusion of, birefringence anisotropies, that could be measured by POLARBEAR, Simons Observatory and LiteBIRD. We also note that cosmic birefringence observables emerge via a Sakharov-like asymmetry, where linear polarization is first generated cosmologically and subsequently twisted by a parity-violating dynamics after last scattering.

Figures

Figures reproduced from arXiv: 2607.27318 by Alexander Westphal, Guido D'Amico, Nemanja Kaloper.

Figure 1
Figure 1. Figure 1: A CMB photon arriving from the last scattering surface. As noted in [16, 29–31], the dark walls naturally support the electromagnetic Chern– Simons terms. Those couplings at low energies can arise either from the mixing of the dark top-form with the visible sector axion/top-form, or by mixing of the visible and dark axions along the lines described above – with the exception that the transmission of the co… view at source ↗
Figure 2
Figure 2. Figure 2: Spectra of C EB ℓ for transitions at different redshifts zPT. Left panel: suppressed reionization; right panel: normal reionization [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Spectra of C EE ℓ for the same transitions as in [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

83 extracted references · 60 linked inside Pith

  1. [1]

    Foundations and Working Pictures in Microphysical Cosmology,

    F. Wilczek, “Foundations and Working Pictures in Microphysical Cosmology,” Phys. Rept. 104, 143 (1984)

    1984

  2. [2]

    The Cosmological Constant Problem,

    S. Weinberg, “The Cosmological Constant Problem,” Rev. Mod. Phys. 61, 1-23 (1989). 24

    1989

  3. [3]

    The Cosmological Constant and the String Landscape,

    J. Polchinski, “The Cosmological Constant and the String Landscape,” [arXiv:hep- th/0603249 [hep-th]]

    arXiv

  4. [4]

    DESI 2024 VI: cosmological constraints from the mea- surements of baryon acoustic oscillations,

    A. G. Adame et al. [DESI], “DESI 2024 VI: cosmological constraints from the mea- surements of baryon acoustic oscillations,” JCAP 02, 021 (2025) [arXiv:2404.03002 [astro-ph.CO]]

    Pith/arXiv arXiv 2024

  5. [5]

    The Hubble Tension and Early Dark Energy,

    M. Kamionkowski and A. G. Riess, “The Hubble Tension and Early Dark Energy,” Ann. Rev. Nucl. Part. Sci. 73, 153-180 (2023) [arXiv:2211.04492 [astro-ph.CO]]

    Pith/arXiv arXiv 2023

  6. [6]

    The String landscape, black holes and gravity as the weakest force,

    N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, “The String landscape, black holes and gravity as the weakest force,” JHEP 06, 060 (2007) [arXiv:hep-th/0601001 [hep-th]]

    Pith/arXiv arXiv 2007

  7. [7]

    Distance and de Sitter Conjectures on the Swampland,

    H. Ooguri, E. Palti, G. Shiu and C. Vafa, “Distance and de Sitter Conjectures on the Swampland,” Phys. Lett. B 788, 180-184 (2019) [arXiv:1810.05506 [hep-th]]

    Pith/arXiv arXiv 2019

  8. [8]

    On the Cosmological Implications of the String Swampland,

    P. Agrawal, G. Obied, P. J. Steinhardt and C. Vafa, “On the Cosmological Implications of the String Swampland,” Phys. Lett. B 784, 271-276 (2018) [arXiv:1806.09718 [hep- th]]

    Pith/arXiv arXiv 2018

  9. [9]

    The Swampland: Introduction and Review,

    E. Palti, “The Swampland: Introduction and Review,” Fortsch. Phys. 67, no.6, 1900037 (2019) [arXiv:1903.06239 [hep-th]]

    Pith/arXiv arXiv 2019

  10. [10]

    Cosmology with ultralight pseudo Nambu-Goldstone bosons,

    J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga, “Cosmology with ultralight pseudo Nambu-Goldstone bosons,” Phys. Rev. Lett. 75, 2077-2080 (1995) [arXiv:astro- ph/9505060 [astro-ph]]

    arXiv 2077

  11. [11]

    Quintessence axion potential induced by elec- troweak instanton effects,

    Y. Nomura, T. Watari and T. Yanagida, “Quintessence axion potential induced by elec- troweak instanton effects,” Phys. Lett. B 484, 103-111 (2000) [arXiv:hep-ph/0004182 [hep-ph]]

    Pith/arXiv arXiv 2000

  12. [12]

    A Quintessential axion,

    J. E. Kim and H. P. Nilles, “A Quintessential axion,” Phys. Lett. B 553, 1-6 (2003) [arXiv:hep-ph/0210402 [hep-ph]]

    Pith/arXiv arXiv 2003

  13. [13]

    Where in the String Landscape is Quintessence,

    N. Kaloper and L. Sorbo, “Where in the String Landscape is Quintessence,” Phys. Rev. D 79, 043528 (2009) [arXiv:0810.5346 [hep-th]]

    Pith/arXiv arXiv 2009

  14. [14]

    Strongly Coupled Quintessence,

    G. D’Amico, N. Kaloper and A. Lawrence, “Strongly Coupled Quintessence,” Phys. Rev. D 100, no.10, 103504 (2019) [arXiv:1809.05109 [hep-th]]

    Pith/arXiv arXiv 2019

  15. [15]

    Quintessence Axion Revisited in Light of Swampland Conjectures,

    M. Ibe, M. Yamazaki and T. T. Yanagida, “Quintessence Axion Revisited in Light of Swampland Conjectures,” Class. Quant. Grav. 36, no.23, 235020 (2019) [arXiv:1811.04664 [hep-th]]

    Pith/arXiv arXiv 2019

  16. [16]

    Discretely evanescent dark energy,

    N. Kaloper, “Discretely evanescent dark energy,” JCAP 11, 075 (2025) [arXiv:2506.04317 [hep-th]]

    Pith/arXiv arXiv 2025

  17. [17]

    On Super-Planckian Fields at Sub-Planckian Energies,

    A. Nicolis, “On Super-Planckian Fields at Sub-Planckian Energies,” JHEP 07, 023 (2008) [arXiv:0802.3923 [hep-th]]. 25

    Pith/arXiv arXiv 2008

  18. [18]

    New physics from the polarized light of the cosmic microwave back- ground,

    E. Komatsu, “New physics from the polarized light of the cosmic microwave back- ground,” Nature Rev. Phys. 4, no.7, 452-469 (2022) [arXiv:2202.13919 [astro-ph.CO]]

    Pith/arXiv arXiv 2022

  19. [19]

    The Structure of Axionic Domain Walls,

    M. C. Huang and P. Sikivie, “The Structure of Axionic Domain Walls,” Phys. Rev. D 32, 1560 (1985)

    1985

  20. [20]

    Effects of a Nambu-Goldstone boson on the polarization of radio galaxies and the cosmic microwave background,

    D. Harari and P. Sikivie, “Effects of a Nambu-Goldstone boson on the polarization of radio galaxies and the cosmic microwave background,” Phys. Lett. B 289, 67-72 (1992)

    1992

  21. [21]

    Quintessence and the rest of the world,

    S. M. Carroll, “Quintessence and the rest of the world,” Phys. Rev. Lett. 81, 3067-3070 (1998) [arXiv:astro-ph/9806099 [astro-ph]]

    Pith/arXiv arXiv 1998

  22. [22]

    Cosmological signature of new parity violating interactions,

    A. Lue, L. M. Wang and M. Kamionkowski, “Cosmological signature of new parity violating interactions,” Phys. Rev. Lett. 83, 1506-1509 (1999) [arXiv:astro-ph/9812088 [astro-ph]]

    Pith/arXiv arXiv 1999

  23. [23]

    Pseudoscalar perturbations and polariza- tion of the cosmic microwave background,

    M. Pospelov, A. Ritz and C. Skordis, “Pseudoscalar perturbations and polariza- tion of the cosmic microwave background,” Phys. Rev. Lett. 103, 051302 (2009) [arXiv:0808.0673 [astro-ph]]

    Pith/arXiv arXiv 2009

  24. [24]

    New Extraction of the Cosmic Birefringence from the Planck 2018 Polarization Data,

    Y. Minami and E. Komatsu, “New Extraction of the Cosmic Birefringence from the Planck 2018 Polarization Data,” Phys. Rev. Lett. 125, no.22, 221301 (2020) [arXiv:2011.11254 [astro-ph.CO]]

    Pith/arXiv arXiv 2018

  25. [25]

    Cosmic birefringence and electroweak axion dark energy,

    G. Choi, W. Lin, L. Visinelli and T. T. Yanagida, “Cosmic birefringence and electroweak axion dark energy,” Phys. Rev. D 104, no.10, L101302 (2021) [arXiv:2106.12602 [hep- ph]]

    Pith/arXiv arXiv 2021

  26. [26]

    Cosmic Birefringence from the Planck Data Release 4,

    P. Diego-Palazuelos, J. R. Eskilt, Y. Minami, M. Tristram, R. M. Sullivan, A. J. Ban- day, R. B. Barreiro, H. K. Eriksen, K. M. Górski and R. Keskitalo, et al. “Cosmic Birefringence from the Planck Data Release 4,” Phys. Rev. Lett. 128, no.9, 091302 (2022) [arXiv:2201.07682 [astro-ph.CO]]

    Pith/arXiv arXiv 2022

  27. [27]

    Cosmic birefringence from monodromic axion dark en- ergy,

    S. Gasparotto and I. Obata, “Cosmic birefringence from monodromic axion dark en- ergy,” JCAP 08, no.08, 025 (2022) [arXiv:2203.09409 [astro-ph.CO]]

    Pith/arXiv arXiv 2022

  28. [28]

    Axionic defects in the CMB: birefringence and gravitational waves,

    R. Z. Ferreira, S. Gasparotto, T. Hiramatsu, I. Obata and O. Pujolas, “Axionic defects in the CMB: birefringence and gravitational waves,” JCAP 05, 066 (2024) [arXiv:2312.14104 [hep-ph]]

    Pith/arXiv arXiv 2024

  29. [29]

    Electromagnetic couplings of dark domain walls,

    N. Kaloper, “Electromagnetic couplings of dark domain walls,” Phys. Rev. D 114, no.1, L011904 (2026) [arXiv:2602.03933 [hep-th]]

    Pith/arXiv arXiv 2026

  30. [30]

    Cloaking Cosmic Light,

    N. Kaloper, “Cloaking Cosmic Light,” [arXiv:2602.20248 [astro-ph.CO]]

    arXiv

  31. [31]

    CMB Birefringence from Vacuum Interfaces,

    N. Kaloper, “CMB Birefringence from Vacuum Interfaces,” [arXiv:2605.11065 [hep-th]]

    Pith/arXiv arXiv

  32. [32]

    Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe,

    A. D. Sakharov, “Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe,” Pisma Zh. Eksp. Teor. Fiz. 5, 32-35 (1967). 26

    1967

  33. [33]

    Axion Dark Matter Detection with CMB Polarization,

    M. A. Fedderke, P. W. Graham and S. Rajendran, “Axion Dark Matter Detection with CMB Polarization,” Phys. Rev. D 100, no.1, 015040 (2019) [arXiv:1903.02666 [astro- ph.CO]]

    Pith/arXiv arXiv 2019

  34. [34]

    Monodromy in the CMB: Gravity Waves and String Inflation,

    E. Silverstein and A. Westphal, “Monodromy in the CMB: Gravity Waves and String Inflation,” Phys. Rev. D 78, 106003 (2008) [arXiv:0803.3085 [hep-th]]

    Pith/arXiv arXiv 2008

  35. [35]

    A Natural Framework for Chaotic Inflation,

    N. Kaloper and L. Sorbo, “A Natural Framework for Chaotic Inflation,” Phys. Rev. Lett. 102, 121301 (2009) [arXiv:0811.1989 [hep-th]]

    Pith/arXiv arXiv 2009

  36. [36]

    Simple exercises to flatten your potential,

    X. Dong, B. Horn, E. Silverstein and A. Westphal, “Simple exercises to flatten your potential,” Phys. Rev. D 84, 026011 (2011) [arXiv:1011.4521 [hep-th]]

    Pith/arXiv arXiv 2011

  37. [37]

    An Ignoble Approach to Large Field Inflation,

    N. Kaloper, A. Lawrence and L. Sorbo, “An Ignoble Approach to Large Field Inflation,” JCAP 03, 023 (2011) [arXiv:1101.0026 [hep-th]]

    Pith/arXiv arXiv 2011

  38. [38]

    The Powers of Monodromy,

    L. McAllister, E. Silverstein, A. Westphal and T. Wrase, “The Powers of Monodromy,” JHEP 09, 123 (2014) [arXiv:1405.3652 [hep-th]]

    Pith/arXiv arXiv 2014

  39. [39]

    Monodromy Inflation in the Strong Cou- pling Regime of the Effective Field Theory,

    G. D’Amico, N. Kaloper and A. Lawrence, “Monodromy Inflation in the Strong Cou- pling Regime of the Effective Field Theory,” Phys. Rev. Lett. 121, no.9, 091301 (2018) [arXiv:1709.07014 [hep-th]]

    Pith/arXiv arXiv 2018

  40. [40]

    Quantum field theory of interacting dark matter and dark energy: Dark monodromies,

    G. D’Amico, T. Hamill and N. Kaloper, “Quantum field theory of interacting dark matter and dark energy: Dark monodromies,” Phys. Rev. D 94, no.10, 103526 (2016) [arXiv:1605.00996 [hep-th]]

    Pith/arXiv arXiv 2016

  41. [41]

    CP Conservation in the Presence of Instantons,

    R. D. Peccei and H. R. Quinn, “CP Conservation in the Presence of Instantons,” Phys. Rev. Lett. 38, 1440-1443 (1977)

    1977

  42. [42]

    A New Light Boson?,

    S. Weinberg, “A New Light Boson?,” Phys. Rev. Lett. 40, 223-226 (1978)

    1978

  43. [43]

    Problem of Strong P and T Invariance in the Presence of Instantons,

    F. Wilczek, “Problem of Strong P and T Invariance in the Presence of Instantons,” Phys. Rev. Lett. 40, 279-282 (1978)

    1978

  44. [44]

    Weak Interaction Singlet and Strong CP Invariance,

    J. E. Kim, “Weak Interaction Singlet and Strong CP Invariance,” Phys. Rev. Lett. 43, 103 (1979)

    1979

  45. [45]

    Can Confinement Ensure Natural CP Invariance of Strong Interactions?,

    M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, “Can Confinement Ensure Natural CP Invariance of Strong Interactions?,” Nucl. Phys. B 166, 493-506 (1980)

    1980

  46. [46]

    On Possible Suppression of the Axion Hadron Interactions. (In Rus- sian),

    A. R. Zhitnitsky, “On Possible Suppression of the Axion Hadron Interactions. (In Rus- sian),” Sov. J. Nucl. Phys. 31, 260 (1980)

    1980

  47. [47]

    A Simple Solution to the Strong CP Problem with a Harmless Axion,

    M. Dine, W. Fischler and M. Srednicki, “A Simple Solution to the Strong CP Problem with a Harmless Axion,” Phys. Lett. B 104, 199-202 (1981)

    1981

  48. [48]

    Solving the Hierarchy Problem Discretely,

    A. Hook, “Solving the Hierarchy Problem Discretely,” Phys. Rev. Lett. 120, no.26, 261802 (2018) [arXiv:1802.10093 [hep-ph]]. 27

    Pith/arXiv arXiv 2018

  49. [49]

    An even lighter QCD axion,

    L. Di Luzio, B. Gavela, P. Quilez and A. Ringwald, “An even lighter QCD axion,” JHEP 05, 184 (2021) [arXiv:2102.00012 [hep-ph]]

    Pith/arXiv arXiv 2021

  50. [50]

    Two U(1)’s and Epsilon Charge Shifts,

    B. Holdom, “Two U(1)’s and Epsilon Charge Shifts,” Phys. Lett. B 166, 196-198 (1986)

    1986

  51. [51]

    The Axidental Universe,

    T. C. Bachlechner, K. Eckerle, O. Janssen and M. Kleban, “The Axidental Universe,” JCAP 03, 050 (2025) [arXiv:1902.05952 [hep-th]]

    Pith/arXiv arXiv 2025

  52. [52]

    PQ axiverse,

    M. Demirtas, N. Gendler, C. Long, L. McAllister and J. Moritz, “PQ axiverse,” JHEP 06, 092 (2023) [arXiv:2112.04503 [hep-th]]

    Pith/arXiv arXiv 2023

  53. [53]

    Large field excursions and approximate discrete symme- tries from a clockwork axion,

    D. E. Kaplan and R. Rattazzi, “Large field excursions and approximate discrete symme- tries from a clockwork axion,” Phys. Rev. D 93, no.8, 085007 (2016) [arXiv:1511.01827 [hep-ph]]

    Pith/arXiv arXiv 2016

  54. [54]

    (De)constructing dimensions,

    N. Arkani-Hamed, A. G. Cohen and H. Georgi, “(De)constructing dimensions,” Phys. Rev. Lett. 86, 4757-4761 (2001) [arXiv:hep-th/0104005 [hep-th]]

    Pith/arXiv arXiv 2001

  55. [55]

    Physical properties of four- dimensional superstring gravity black hole solutions,

    B. A. Campbell, N. Kaloper, R. Madden and K. A. Olive, “Physical properties of four- dimensional superstring gravity black hole solutions,” Nucl. Phys. B 399, 137-168 (1993) [arXiv:hep-th/9301129 [hep-th]]

    Pith/arXiv arXiv 1993

  56. [56]

    Naturally inflating on steep potentials through electro- magnetic dissipation,

    M. M. Anber and L. Sorbo, “Naturally inflating on steep potentials through electro- magnetic dissipation,” Phys. Rev. D 81, 043534 (2010) [arXiv:0908.4089 [hep-th]]

    Pith/arXiv arXiv 2010

  57. [57]

    Mixing of the Photon with Low Mass Particles,

    G. Raffelt and L. Stodolsky, “Mixing of the Photon with Low Mass Particles,” Phys. Rev. D 37, 1237 (1988)

    1988

  58. [58]

    On the possibility of large axion decay constants,

    T. Banks, M. Dine, P. J. Fox and E. Gorbatov, “On the possibility of large axion decay constants,” JCAP 06, 001 (2003) [arXiv:hep-th/0303252 [hep-th]]

    Pith/arXiv arXiv 2003

  59. [59]

    Sharpening the Weak Gravity Conjecture with Dimensional Reduction,

    B. Heidenreich, M. Reece and T. Rudelius, “Sharpening the Weak Gravity Conjecture with Dimensional Reduction,” JHEP 02, 140 (2016) [arXiv:1509.06374 [hep-th]]

    Pith/arXiv arXiv 2016

  60. [60]

    Evidence for a sublattice weak gravity conjecture,

    B. Heidenreich, M. Reece and T. Rudelius, “Evidence for a sublattice weak gravity conjecture,” JHEP 08, 025 (2017) [arXiv:1606.08437 [hep-th]]

    Pith/arXiv arXiv 2017

  61. [61]

    The Weak Gravity Conjecture in three dimensions,

    M. Montero, G. Shiu and P. Soler, “The Weak Gravity Conjecture in three dimensions,” JHEP 10, 159 (2016) [arXiv:1606.08438 [hep-th]]

    Pith/arXiv arXiv 2016

  62. [62]

    A Tower Weak Gravity Conjecture from Infrared Consistency,

    S. Andriolo, D. Junghans, T. Noumi and G. Shiu, “A Tower Weak Gravity Conjecture from Infrared Consistency,” Fortsch. Phys. 66, no.5, 1800020 (2018) [arXiv:1802.04287 [hep-th]]

    Pith/arXiv arXiv 2018

  63. [63]

    Weak gravity conjecture,

    D. Harlow, B. Heidenreich, M. Reece and T. Rudelius, “Weak gravity conjecture,” Rev. Mod. Phys. 95, no.3, 3 (2023) [arXiv:2201.08380 [hep-th]]

    Pith/arXiv arXiv 2023

  64. [64]

    Axion Monodromy and the Weak Gravity Conjecture,

    A. Hebecker, F. Rompineve and A. Westphal, “Axion Monodromy and the Weak Gravity Conjecture,” JHEP 04, 157 (2016) [arXiv:1512.03768 [hep-th]]. 28

    Pith/arXiv arXiv 2016

  65. [65]

    Positivity of the gravitational path integral implies the axionic weak gravity conjecture,

    G. Di Ubaldo, L. V. Iliesiu, H. W. Lin and C. Yan, “Positivity of the gravitational path integral implies the axionic weak gravity conjecture,” [arXiv:2605.05305 [hep-th]]

    Pith/arXiv arXiv

  66. [66]

    Wormholes and the imaginary distance bound,

    J. Maldacena, A. Maloney and B. McPeak, “Wormholes and the imaginary distance bound,” [arXiv:2605.05336 [hep-th]]

    Pith/arXiv arXiv

  67. [67]

    Generalized theory of interference, and its applications,

    S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. In- dian Acad. Sci. A 44, no.5, 247-262 (1956)

    1956

  68. [68]

    Generalized theory of interference and its applications. part ii. par- tially coherent pencils,

    S. Pancharatnam, “Generalized theory of interference and its applications. part ii. par- tially coherent pencils,” Proc. Indian Acad. Sci. - Section A 44, 398-417 (1956)

    1956

  69. [69]

    The Secret Long Range Force in Quantum Field Theories With Instan- tons,

    M. Luscher, “The Secret Long Range Force in Quantum Field Theories With Instan- tons,” Phys. Lett. B 78, 465-467 (1978)

    1978

  70. [70]

    Modeling the glueball spectrum by a closed bosonic membrane,

    G. Gabadadze, “Modeling the glueball spectrum by a closed bosonic membrane,” Phys. Rev. D 58, 094015 (1998) [arXiv:hep-ph/9710402 [hep-ph]]

    Pith/arXiv arXiv 1998

  71. [71]

    QCD vacuum and axions: What’s happening?,

    G. Gabadadze and M. Shifman, “QCD vacuum and axions: What’s happening?,” Int. J. Mod. Phys. A 17, 3689-3728 (2002) [arXiv:hep-ph/0206123 [hep-ph]]

    Pith/arXiv arXiv 2002

  72. [72]

    Could the Universe Have Recovered from a Slow First Order Phase Transition?,

    A. H. Guth and E. J. Weinberg, “Could the Universe Have Recovered from a Slow First Order Phase Transition?,” Nucl. Phys. B 212, 321-364 (1983)

    1983

  73. [73]

    Bubble nucleation in first order inflation and other cosmological phase transitions,

    M. S. Turner, E. J. Weinberg and L. M. Widrow, “Bubble nucleation in first order inflation and other cosmological phase transitions,” Phys. Rev. D 46, 2384-2403 (1992)

    1992

  74. [74]

    Constraints on anisotropic cosmic bire- fringence from CMB B-mode polarization,

    A. I. Lonappan, B. Keating and K. Arnold, “Constraints on anisotropic cosmic bire- fringence from CMB B-mode polarization,” Phys. Rev. D 112, no.2, 023555 (2025) [arXiv:2504.13154 [astro-ph.CO]]

    Pith/arXiv arXiv 2025

  75. [75]

    Is cosmic birefringence due to dark energy or dark matter? A tomographic approach,

    H. Nakatsuka, T. Namikawa and E. Komatsu, “Is cosmic birefringence due to dark energy or dark matter? A tomographic approach,” Phys. Rev. D 105, no.12, 123509 (2022) [arXiv:2203.08560 [astro-ph.CO]]

    Pith/arXiv arXiv 2022

  76. [76]

    Alternative to axions,

    N. Kaloper, “Alternative to axions,” Phys. Rev. D 113, no.1, L011701 (2026) [arXiv:2504.21078 [hep-ph]]

    arXiv 2026

  77. [77]

    Quantal theory of restoration of strong CP symmetry,

    N. Kaloper, “Quantal theory of restoration of strong CP symmetry,” Phys. Rev. D 113, no.7, 7 (2026) [arXiv:2505.04690 [hep-ph]]

    Pith/arXiv arXiv 2026

  78. [78]

    Tomographic constraint on anisotropic cosmic birefringence,

    T. Namikawa, “Tomographic constraint on anisotropic cosmic birefringence,” Phys. Rev. D 111, no.2, 2 (2025) [arXiv:2410.05149 [astro-ph.CO]]

    Pith/arXiv arXiv 2025

  79. [79]

    Cosmic birefringence tomography and calibration independence with reionization signals in the CMB,

    B. D. Sherwin and T. Namikawa, “Cosmic birefringence tomography and calibration independence with reionization signals in the CMB,” Mon. Not. Roy. Astron. Soc. 520, no.3, 3298-3304 (2023) [arXiv:2108.09287 [astro-ph.CO]]

    Pith/arXiv arXiv 2023

  80. [80]

    Universal Profile for Cosmic Birefringence Tomography with Radio Galax- ies,

    F. Naokawa, “Universal Profile for Cosmic Birefringence Tomography with Radio Galax- ies,” Phys. Rev. Lett. 136, no.4, 041004 (2026) [arXiv:2504.06709 [astro-ph.CO]]. 29

    Pith/arXiv arXiv 2026

Showing first 80 references.