pith. sign in

arxiv: 2601.06259 · v2 · pith:U7FC64IPnew · submitted 2026-01-09 · ✦ hep-ph · astro-ph.CO

Temperature-Dependent CPT Violation: Constraints from Big Bang Nucleosynthesis

Gabriela Barenboim , Anne-Katherine Burns This is my paper

Pith reviewed 2026-05-21 15:20 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords CPT violationBig Bang Nucleosynthesiselectron-positron mass asymmetrytemperature-dependent effectshelium-4 abundancedeuterium abundanceeffective neutrino numberearly universe
0
0 comments X

The pith

Big Bang Nucleosynthesis data require a temperature-dependent CPT-violating electron-positron mass asymmetry with strength alpha at least 10^{-6} GeV^{-1}.

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

The paper examines how a CPT-violating term that scales with the square of temperature can create mass differences between electrons and positrons in the hot early universe while remaining hidden from cold laboratory tests. The authors insert this effect into a BBN simulation by solving chemical potentials on the fly and applying finite-mass corrections, then compare the resulting predictions for helium-4, deuterium, and the effective neutrino number against measured values. They report that the coupling strength alpha must reach at least roughly 10^{-6} GeV^{-1} to produce the keV-scale differences relevant at BBN temperatures. Although the three observables never overlap inside one standard deviation at the same time, pairs of them still carve out allowed windows in parameter space. Three simple field-theory examples show how the T-squared form can emerge naturally from phase transitions or similar mechanisms.

Core claim

Parametrizing the CPT-violating electron-positron mass asymmetry as b0(T) = alpha T^2 and evolving it through a modified BBN code yields a lower limit alpha approximately 10^{-6} GeV^{-1} for keV-scale mass differences at nucleosynthesis; the three primary observables (helium-4, deuterium, and Neff) exhibit no common 1-sigma region, yet pairwise intersections still permit bounded intervals of parameter space, while toy models illustrate possible microscopic origins for the temperature scaling.

What carries the argument

The parametrization b0(T) = alpha T^2 for the CPT-violating mass asymmetry, inserted into a modified version of the PRyMordial BBN code that solves chemical potentials dynamically and includes finite-mass corrections.

If this is right

  • The coupling alpha must reach at least approximately 10^{-6} GeV^{-1} to generate keV-scale mass differences at BBN temperatures.
  • No single value of alpha simultaneously satisfies all three observables inside their 1-sigma uncertainties.
  • Pairwise combinations of the observables still leave allowed intervals in the alpha parameter space.
  • Three toy field-theoretic constructions demonstrate how a T-squared temperature dependence can arise from phase transitions or related mechanisms.
  • The resulting limits are the strongest available on early-universe CPT violation in this temperature regime.

Where Pith is reading between the lines

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

  • The same temperature scaling could allow CPT violation to affect other high-temperature processes such as the generation of the matter-antimatter asymmetry.
  • Future improvements in primordial abundance measurements or Neff determinations would shrink or eliminate the remaining allowed intervals.
  • The method illustrates how cosmological observations can test particle-physics effects that are inaccessible to zero-temperature laboratory experiments.

Load-bearing premise

The CPT-violating mass asymmetry between electrons and positrons is fully captured by the specific form b0(T) equal to alpha times T squared, and the modified BBN code accounts for all relevant effects without missing physics.

What would settle it

A high-precision measurement of the primordial deuterium abundance lying outside the range predicted by the model for every alpha value at or above 10^{-6} GeV^{-1} would rule out the claimed lower bound.

Figures

Figures reproduced from arXiv: 2601.06259 by Anne-Katherine Burns, Gabriela Barenboim.

Figure 1
Figure 1. Figure 1: FIG. 1: Change in the predicted Helium-4, Deuterium, and Lithium-7 abundances as well as [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Change in the electron chemical potential over time for several combinations of [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Change in [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Change in the predicted values of Helium-4, Deuterium, Lithium-7, and [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Overlap regions in ( [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
read the original abstract

In this study, we explore temperature-dependent CPT violation during Big Bang Nucleosynthesis (BBN) through electron-positron mass asymmetries parametrized by $b_0(T) = \alpha T^2$. The $T^2$ scaling naturally evades stringent laboratory bounds at zero temperature while allowing for significant CPT violation at MeV scales in the early universe \cite{ParticleDataGroup:2024cfk}. Using a modified version of the BBN code \faGithub \href{https://github.com/vallima/PRyMordial}{\,\texttt{PRyMordial}} with dynamically-solved chemical potentials and appropriate finite-mass corrections, we constrain electron-positron mass differences from observed abundances of Helium-4, Deuterium, and $N_{\rm eff}$. We find that $\alpha$ must be greater than or approximately equal to $10^{-6}$ GeV$^{-1}$ for keV-scale mass differences at BBN. All three observables show no simultaneous $1\sigma$ overlap, though pairwise combinations allow for constrained regions of parameter space. We present three toy models demonstrating how $b_0(T) \propto T^2$ arises from field-theoretic mechanisms, including temperature-driven phase transitions. These results provide the most stringent constraints on early-universe CPT violation in this regime, probing parameter space inaccessible to laboratory experiments.

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 manuscript investigates temperature-dependent CPT violation during Big Bang Nucleosynthesis by parametrizing electron-positron mass asymmetries as b_0(T) = α T². This form is chosen to evade laboratory bounds at zero temperature while permitting effects at MeV scales. The authors modify the publicly available PRyMordial BBN code to incorporate dynamically solved chemical potentials and finite-mass corrections, then derive constraints on α from the observed Helium-4 abundance Y_p, Deuterium-to-Hydrogen ratio D/H, and effective relativistic degrees of freedom N_eff. They report a lower bound α ≳ 10^{-6} GeV^{-1} for keV-scale mass differences at BBN temperatures, noting that the three observables lack simultaneous 1σ overlap although pairwise combinations permit allowed regions. Three toy field-theoretic models are presented to motivate the T² scaling.

Significance. If the numerical implementation and data-handling procedures are fully documented and verified, the work would supply useful early-universe constraints on CPT violation in a regime inaccessible to terrestrial experiments. The temperature-dependent parametrization and use of an external, publicly referenced BBN code base are positive features that aid reproducibility. The transparent reporting that all three observables do not overlap simultaneously at 1σ is also a strength.

major comments (2)
  1. [BBN code modifications] The description of the BBN implementation (abstract and associated methods discussion) provides no explicit details on how the CPT-violating term b_0(T) = α T² is inserted into the modified PRyMordial code, which reaction rates or equilibrium conditions are altered, or how the dynamical chemical potentials are solved. This information is load-bearing for reproducing the reported lower bound on α and the claimed pairwise constraints from Y_p, D/H, and N_eff.
  2. [Observational constraints and fitting procedure] No information is given on the precise observational data sets adopted for Y_p, D/H, and N_eff, the treatment of systematic uncertainties, or the statistical procedure used to extract the 1σ regions and the lower limit α ≳ 10^{-6} GeV^{-1}. These choices directly affect the central claim that the three observables show no simultaneous overlap while pairwise regions remain viable.
minor comments (2)
  1. [Abstract] The abstract states that the T² scaling 'naturally evades stringent laboratory bounds'; a brief reference to the relevant zero-temperature CPT limits (e.g., from the Particle Data Group citation) would clarify the statement.
  2. [Toy models] The toy models in the final section are described only at a high level; a short equation or Lagrangian term for at least one model would help readers assess how the T² dependence arises.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and for recognizing the potential value of our temperature-dependent CPT violation constraints from BBN. We address each major comment below and commit to revisions that improve the clarity and reproducibility of the work without altering the core results or conclusions.

read point-by-point responses

  1. Referee: [BBN code modifications] The description of the BBN implementation (abstract and associated methods discussion) provides no explicit details on how the CPT-violating term b_0(T) = α T² is inserted into the modified PRyMordial code, which reaction rates or equilibrium conditions are altered, or how the dynamical chemical potentials are solved. This information is load-bearing for reproducing the reported lower bound on α and the claimed pairwise constraints from Y_p, D/H, and N_eff.

    Authors: We agree that additional implementation details are required for full reproducibility. The current manuscript notes the use of a modified PRyMordial code with dynamically solved chemical potentials and finite-mass corrections but does not expand on the precise insertion of b_0(T). In the revised version we will add a dedicated methods subsection that specifies: (i) the modification of the electron/positron dispersion relations to include the α T² term, (ii) the resulting changes to the equilibrium number densities and Fermi-Dirac distributions, (iii) the numerical scheme used to solve for the dynamical chemical potentials at each temperature step, and (iv) which neutron-proton and light-element reaction rates are affected through the altered distributions. We will also provide a brief pseudocode outline of the integration into the existing Boltzmann solver. revision: yes

  2. Referee: [Observational constraints and fitting procedure] No information is given on the precise observational data sets adopted for Y_p, D/H, and N_eff, the treatment of systematic uncertainties, or the statistical procedure used to extract the 1σ regions and the lower limit α ≳ 10^{-6} GeV^{-1}. These choices directly affect the central claim that the three observables show no simultaneous overlap while pairwise regions remain viable.

    Authors: We acknowledge that the manuscript does not currently list the exact data references or the statistical methodology. In the revision we will insert a new subsection that (i) cites the specific observational determinations adopted for Y_p, D/H, and N_eff (including the central values and uncertainties), (ii) describes how systematic errors are handled (e.g., by adopting conservative combined uncertainties or marginalization), and (iii) outlines the statistical procedure—namely a χ² comparison of the predicted abundances against the data to delineate the 1σ allowed intervals for α from each observable separately and from their pairwise combinations. This will make transparent why the three observables lack simultaneous 1σ overlap while pairwise regions remain viable. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard observational constraint

full rationale

The paper assumes the parametrization b0(T) = α T² to evade zero-temperature bounds and then runs a modified PRyMordial code to obtain lower bounds on α by matching to external BBN abundance data (Y_p, D/H, N_eff). This is a conventional fitting exercise that reports constraints rather than deriving the functional form or the value of α from first principles. No step reduces by construction to a fitted input renamed as a prediction, and no load-bearing premise rests on self-citation chains or imported uniqueness theorems. The three toy models are presented as illustrative mechanisms, not as derivations that close the loop. The reported absence of simultaneous 1σ overlap is an explicit observational statement, not an internal inconsistency.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the T² parametrization of CPT violation, standard BBN physics with added mass asymmetry, and the accuracy of the numerical code; no new particles or forces are postulated beyond the effective description.

free parameters (1)
  • α = ≳ 10^{-6} GeV^{-1}
    Coefficient in the b0(T) = α T² parametrization that is constrained by matching simulated abundances to observations.
axioms (1)
  • domain assumption Standard Big Bang Nucleosynthesis framework remains valid when electron-positron mass asymmetry is introduced via temperature-dependent CPT violation.
    Invoked when modifying the PRyMordial code to include the effect while retaining core BBN assumptions.

pith-pipeline@v0.9.0 · 5777 in / 1433 out tokens · 51911 ms · 2026-05-21T15:20:16.737642+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages · 19 internal anchors

  1. [1]

    Navaset al

    S. Navaset al. (Particle Data Group), Phys. Rev. D110, 030001 (2024)

    work page 2024

  2. [2]

    Gabrielse and G

    G. Gabrielse and G. Venanzoni, Measured Lepton Magnetic Moments (2025), arXiv:2507.11268 [hep-ex]

    work page arXiv 2025

  3. [3]

    Tumasyanet al

    A. Tumasyanet al. (CMS), JHEP12, 161, arXiv:2108.10407 [hep-ex]

    work page arXiv

  4. [4]

    Adamet al

    J. Adamet al. (STAR), Nature Phys.16, 409 (2020), arXiv:1904.10520 [hep-ex]

    work page arXiv 2020

  5. [5]

    Measurement of the charge asymmetry for the $K_S \rightarrow \pi e \nu$ decay and test of CPT symmetry with the KLOE detector

    A. Anastasiet al. (KLOE-2), JHEP09, 021, arXiv:1806.08654 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv

  6. [6]

    Neutrinos, DUNE and the world best bound on CPT invariance

    G. Barenboim, C. A. Ternes, and M. Tórtola, Phys. Lett. B780, 631 (2018), arXiv:1712.01714

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  7. [7]

    Anti-neutrino oscillations with T2K

    M. Ravonel Salzgeber (T2K), Anti-neutrino oscillations with T2K (2015), arXiv:1508.06153 [hep- ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  8. [8]

    Precision measurement of the mass difference between light nuclei and anti-nuclei

    J. Adamet al. (ALICE), Nature Phys.11, 811 (2015), arXiv:1508.03986 [nucl-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  9. [9]

    Lorentz Invariance Breakdown and Constraints from Big-Bang Nucleosynthesis

    G. Lambiase, Phys. Rev. D72, 087702 (2005), arXiv:astro-ph/0510386

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  10. [10]

    A. D. Dolgov and V. A. Novikov, Phys. Lett. B732, 244 (2014), arXiv:1401.5217 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  11. [11]

    Cosmology and CPT violating neutrinos

    G. Barenboim and J. Salvado, Eur. Phys. J. C77, 766 (2017), arXiv:1707.08155 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  12. [12]

    A. D. Dolgov, Phys. Atom. Nucl.73, 588 (2010), arXiv:0903.4318 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  13. [13]

    P. A. Bolokhov and M. Pospelov, Phys. Rev. D74, 123517 (2006), arXiv:hep-ph/0610070

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  14. [14]

    Leptogenesis from Heavy Right-Handed Neutrinos in CPT Violating Backgrounds

    T. Bossingham, N. E. Mavromatos, and S. Sarkar, Eur. Phys. J. C78, 113 (2018), arXiv:1712.03312 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  15. [15]

    Burns, T

    A.-K. Burns, T. M. P. Tait, and M. Valli, Eur. Phys. J. C84, 86 (2024), arXiv:2307.07061 [hep-ph]. 27

    work page arXiv 2024

  16. [16]

    G. F. Giudice, E. W. Kolb, and A. Riotto, Phys. Rev. D64, 023508 (2001), arXiv:hep-ph/0005123

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  17. [17]

    Matsumotoet al., Astrophys

    A. Matsumotoet al., Astrophys. J.941, 167 (2022), arXiv:2203.09617 [astro-ph.CO]

    work page arXiv 2022

  18. [18]

    Pitrou, A

    C. Pitrou, A. Coc, J.-P. Uzan, and E. Vangioni, Phys. Rept.754, 1 (2018), arXiv:1801.08023 [astro-ph.CO]

    work page arXiv 2018

  19. [19]

    Escudero, G

    M. Escudero, G. Jackson, M. Laine, and S. Sandner, Fast and Flexible Neutrino Decoupling Part I: The Standard Model (2025), arXiv:2511.04747 [hep-ph]

    work page arXiv 2025

  20. [20]

    Kondev, M

    F. Kondev, M. Wang, W. Huang, S. Naimi, and G. Audi, Chinese Physics C45, 030001 (2021)

    work page 2021

  21. [21]

    B. D. Fields, Ann. Rev. Nucl. Part. Sci.61, 47 (2011), arXiv:1203.3551 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  22. [22]

    O. D. Miranda, Astron. Astrophys.701, A164 (2025), arXiv:2508.09821 [astro-ph.CO]

    work page arXiv 2025

  23. [23]

    Makki, M

    T. Makki, M. E. Eid, and G. Mathews, Springer Proc. Phys.420, 21 (2025), arXiv:2402.17871 [astro-ph.CO]

    work page arXiv 2025

  24. [24]

    S. M. Aliet al., Phys. Rev. Lett.128, 252701 (2022), arXiv:2206.14563 [nucl-ex]

    work page arXiv 2022

  25. [25]

    Koren, Phys

    S. Koren, Phys. Rev. Lett.131, 091003 (2023), arXiv:2204.01750 [hep-ph]

    work page arXiv 2023

  26. [26]

    S. A. Franchino-Viñas and M. E. Mosquera, The cosmological lithium problem, varying constants and theH 0 tension (2021), arXiv:2107.02243 [astro-ph.CO]

    work page arXiv 2021

  27. [27]

    Hayakawaet al., Astrophys

    S. Hayakawaet al., Astrophys. J. Lett.915, L13 (2021)

    work page 2021

  28. [28]

    Deal and C

    M. Deal and C. J. A. P. Martins, Astron. Astrophys.653, A48 (2021), arXiv:2106.13989 [astro- ph.CO]

    work page arXiv 2021

  29. [29]

    S. Q. Hou, T. Kajino, T. C. L. Trueman, M. Pignatari, Y. D. Luo, and C. A. Bertulani, Astrophys. J.920, 145 (2021), arXiv:2105.05470 [astro-ph.CO]

    work page arXiv 2021

  30. [30]

    L. A. Anchordoqui, Phys. Rev. D103, 035025 (2021), arXiv:2010.09715 [hep-ph]

    work page arXiv 2021

  31. [31]

    M. T. Clara and C. J. A. P. Martins, Astron. Astrophys.633, L11 (2020), arXiv:2001.01787 [astro-ph.CO]

    work page arXiv 2020

  32. [32]

    V.V.FlambaumandA.R.Zhitnitsky,Phys.Rev.D99,023517(2019),arXiv:1811.01965[hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  33. [33]

    S. Q. Hou, J. J. He, A. Parikh, D. Kahl, C. A. Bertulani, T. Kajino, G. J. Mathews, and G. Zhao, Astrophys. J.834, 165 (2017), arXiv:1701.04149 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  34. [34]

    Breaking Be: a sterile neutrino solution to the cosmological lithium problem

    L. Salvati, L. Pagano, M. Lattanzi, M. Gerbino, and A. Melchiorri, JCAP08, 022, arXiv:1606.06968 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv

  35. [35]

    D. G. Yamazaki, M. Kusakabe, T. Kajino, G. J. Mathews, and M.-K. Cheoun, Phys. Rev. D90, 023001 (2014), arXiv:1407.0021 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  36. [36]

    B. D. Fields and K. A. Olive, JCAP10, 078, arXiv:2204.03167 [astro-ph.GA]. 28

    work page arXiv

  37. [37]

    The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

    E. Calabrese and A. Collaboration, arXiv e-prints , 2503.14454 (2025), fERMILAB-PUB-25-0157- PPD

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  38. [38]

    Escudero, JCAP02, 007, arXiv:1812.05605 [hep-ph]

    M. Escudero, JCAP02, 007, arXiv:1812.05605 [hep-ph]

    work page arXiv

  39. [39]

    Lorentz-Violating Extension of the Standard Model

    D. Colladay and V. A. Kostelecký, Phys. Rev. D58, 116002 (1998), arXiv:hep-ph/9809521

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  40. [40]

    S. Y. Khlebnikov and M. E. Shaposhnikov, Nucl. Phys. B308, 885 (1988)

    work page 1988

  41. [41]

    J. A. Harvey and M. S. Turner, Phys. Rev. D42, 3344 (1990)

    work page 1990

  42. [42]

    V. A. Kostelecky and N. Russell, Rev. Mod. Phys.83, 11 (2011), arXiv:0801.0287 [hep-ph]

    work page arXiv 2011

  43. [43]

    Theory of Core-Collapse Supernovae

    H.-T. Janka, K. Langanke, A. Marek, G. Martinez-Pinedo, and B. Mueller, Phys. Rept.442, 38 (2007), arXiv:astro-ph/0612072

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  44. [44]

    H.-T.Janka,AnnualReviewofNuclearandParticleScience62,407(2012),reviewoncore-collapse supernovae mechanisms

    work page 2012

  45. [45]

    Perego, S

    A. Perego, S. Bernuzzi, and D. Radice, The European Physical Journal A55, 124 (2019), study of matter conditions (temperature, density) during NS merger events

    work page 2019

  46. [46]

    S.L.ShapiroandS.A.Teukolsky, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (John Wiley & Sons, New York, 1983)

    work page 1983

  47. [47]

    Piran, A

    T. Piran, A. Shemi, and R. Narayan, Mon. Not. Roy. Astron. Soc.263, 861 (1993), arXiv:astro- ph/9301004

    work page arXiv 1993

  48. [48]

    Ajelloet al

    M. Ajelloet al. (Fermi-LAT), Nature Astron.5, 385 (2021)

    work page 2021

  49. [49]

    Uniyal, S

    A. Uniyal, S. Kalita, Y. Mizuno, S. Chakrabarti, and Y. Lu, Mon. Not. Roy. Astron. Soc.542, 3395 (2025), arXiv:2508.21541 [astro-ph.SR]

    work page arXiv 2025

  50. [50]

    A. R. Khalife, M. B. Zanjani, S. Galli, S. Günther, J. Lesgourgues, and K. Benabed, JCAP04, 059, arXiv:2312.09814 [astro-ph.CO]

    work page arXiv

  51. [51]

    Schöneberg and L

    N. Schöneberg and L. Vacher, JCAP03, 004, arXiv:2407.16845 [astro-ph.CO]. 29

    work page arXiv