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A glitch in gravity: cosmic Lorentz-violation from fiery Big Bang to glacial heat death

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Cosmic data favor gravity that is one percent weaker beyond the Hubble horizon.

desk verdict A competent, honest constraint update of the same glitch model, with a load-bearing fluid approximation that the authors do not fully defend. read the letter →

arxiv 2412.09568 v1 pith:QBVD6I6O submitted 2024-12-12 astro-ph.CO gr-qchep-th

Robin Y. Wen , Lukas T. Hergt , Niayesh Afshordi , Douglas Scott This is my paper · ORCID
classification astro-ph.COgr-qchep-th
keywords cosmicglitchLorentzviolationsuperhorizongravityHubbletensionclusteringmicrowavebackgroundbaryonacousticoscillations
topics Dark EnergyThe Hubble Tension
open problems Dark Energy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether gravity could have a different strength on scales larger than the cosmological horizon than it does inside the horizon, and it shows that current cosmological data mildly prefer that it does. In a one-parameter extension of the standard cold-dark-matter model with a cosmological constant, the cosmic glitch parameter $\Omega_g \equiv 1 - G_N/G_{\rm cosmo}$ measures how much superhorizon gravity differs from subhorizon gravity. Planck 2018 CMB data prefer $\Omega_g = -0.0087 \pm 0.0046$, and a combination of CMB, BAO including DESI Y1, supernova, lensing, and distance-ladder data gives $\Omega_g = -0.0059 \pm 0.0027$, a roughly $2\sigma$ preference for weaker gravity. If the preference is real, the same parameter eases the Hubble tension from $4.1\sigma$ to $3.0\sigma$ and relaxes the $S_8$-$\Omega_m$ clustering tension, and it connects to a stronger glitch during Big Bang nucleosynthesis.

What carries the argument

The load-bearing object is the cosmic glitch parameter $\Omega_g$ inserted into the Friedmann equation as $H^2 = (8\pi G_N/3)(\rho_{\rm tot} + \Omega_g \rho_{\rm crit})$, so the expansion rate responds to the total density with an effective gravitational strength $G_{\rm cosmo} = G_N/(1-\Omega_g)$. This one-number extension is the low-energy signature of Lorentz-violating gravity theories such as cuscuton, Hořava–Lifshitz, and Einstein-Aether, whose deviations from general relativity are screened below the Hubble scale. To predict the CMB, the glitch is treated as an additional perfect dark-energy fluid within the parameterized post-Friedmann (PPF) framework, with rest-frame sound speed $c_s^2 = 1$; the integrated Sachs-Wolfe effect at low multipoles (the temperature change CMB photons pick up crossing time-varying potentials) is the channel through which the data constrain $\Omega_g$.

What would settle it

Compute the CMB temperature power spectrum at $\ell < 100$ directly from an explicit Einstein-Aether or cuscuton action at fixed $G_{\rm cosmo}/G_N$; if the predicted integrated Sachs-Wolfe signal differs from the PPF perfect-fluid prediction by more than cosmic variance, the fitted $\Omega_g$ is an artifact of the effective parametrization. A cosmic-variance-limited measurement of $\Omega_g$ consistent with zero at $\sigma < 10^{-3}$ would likewise remove the current preference.

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Extended reading notes

Core claim

The central claim is that the data favor a universe in which gravity is slightly weaker on superhorizon scales than on subhorizon scales, with the ratio encoded by $\Omega_g \equiv 1 - G_N/G_{\rm cosmo}$. A fit to Planck 2018 gives $\Omega_g = -0.0087 \pm 0.0046$, i.e. $G_{\rm cosmo}/G_N = 0.9914 \pm 0.0045$; combining all datasets yields $\Omega_g = -0.0059 \pm 0.0027$. The preference remains at about the $2\sigma$ level when the assumed dark-energy sound speed is varied from $c_s^2 = 0.1$ to $10$. The glitch also reaches back to Big Bang nucleosynthesis, where EMPRESS helium-abundance data require $\Omega_g = -0.085 \pm 0.027$, an order of magnitude stronger, which the authors interpret as evidence for a logarithmic running of the glitch with scale: maximum at the Big Bang, and nearly vanishing at the de Sitter radius of today's dark energy.

Load-bearing premise

The result stands on the assumption that a single smooth fluid with sound speed essentially that of light faithfully reproduces how real Lorentz-violating gravity theories perturb the CMB on superhorizon scales, so that the fitted $\Omega_g$ actually measures $G_{\rm cosmo}/G_N$.

Editorial extensions

If this is right

  • A superhorizon gravity about one percent weaker than general relativity moves the Planck-inferred Hubble constant from $4.1\sigma$ to $3.0\sigma$ away from the local distance-ladder value, and Planck plus Dark Energy Survey data fit within $2.4\sigma$.
  • The measured $S_8$-$\Omega_m$ contours from DES and Planck overlap more under the glitch model, reducing the clustering tension in that parameter plane.
  • Including BAO data, DESI Y1 among them, tightens the glitch to $\Omega_g = -0.0067 \pm 0.0029$ with Planck PR4, showing the preference survives newer large-scale structure data.
  • If the glitch runs logarithmically with scale, the BBN constraint $\Omega_g = -0.085 \pm 0.027$ together with the CMB constraint implies near-vanishing Lorentz violation at the de Sitter radius and order-one violation near the Planck scale.
  • Stage-IV CMB and Euclid-like BAO surveys are forecast to shrink the uncertainty on $\Omega_g$ below $10^{-3}$, enough to test whether the glitch is real or a statistical fluctuation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct test of the paper's mapping would be to evolve superhorizon perturbations in the full Einstein-Aether or cuscuton theory and compare the resulting CMB power at $\ell < 100$ with the PPF perfect-fluid prediction at the same $G_{\rm cosmo}/G_N$; disagreement beyond cosmic variance would mean the $\Omega_g$ constraint is an artifact of the fluid description.
  • If the glitch is real, its signature should also appear in CMB lensing and in the large-angle kinetic Sunyaev-Zeldovich effect, the secondary temperature distortion from ionized gas, providing independent checks of the integrated Sachs-Wolfe signal that carries the current constraint.
  • The logarithmic-running scenario suggests a concrete extension: measuring the primordial helium abundance across multiple low-metallicity systems at different redshifts would trace $\Omega_g$ at several nucleosynthesis epochs, testing whether the scale dependence is logarithmic rather than a single offset.
  • A positive glitch would produce an enhanced rather than suppressed large-scale ISW signal, so a future high-precision measurement of the low-multipole CMB temperature spectrum that finds an excess would falsify the preferred sign of the model.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper studies a single-parameter extension to ΛCDM, the 'cosmic glitch in gravity' (CGG) model, in which the Friedmann equation is modified by Ω_g = 1 − G_N/G_cosmo and reformulated as an effective dark-energy component. The authors modify CAMB, use the PPF double-field prescription with c_s^2 = 1, and run PolyChord/Cobaya nested sampling against Planck18, Planck PR4, BAO (Stage-III and DESI Y1), Pantheon+ SNe, DES Y1, and SH0ES. They report Ω_g = −0.0087 ± 0.0046 for Planck18, corresponding to G_cosmo/G_N = 0.9914 ± 0.0045, and Ω_g = −0.0067 ± 0.0029 for PR4+DESI Y1 BAO, with a combined 'All' value of Ω_g = −0.0059 ± 0.0027. They further report that the model eases the H0 tension from 4.1σ to 3.0σ and partly reconciles DES and Planck in the S8–Ωm plane, and they connect the negative Ω_g to a BBN value from EMPRESS, suggesting a logarithmic running.

Significance. If the CMB/BAO preference is real, the CGG model would be an economical hint that gravitational strength differs on super- and sub-horizon scales, and the forecast that Stage-IV data can reach σ(Ω_g) < 10^−3 is a falsifiable prediction. The paper follows standard Bayesian parameter estimation, reports robustness checks on c_s^2, and is transparent about the modest significance of the preference. The main caveat is that the fitted Ω_g is interpreted as G_cosmo/G_N through an assumed perfect-fluid description; without validation against the linear perturbation equations of the motivating Lorentz-violating theories, the claim is a phenomenological fit rather than a test of those theories.

major comments (3)
  1. [Section 2, PPF implementation] The mapping from the CGG fluid to the fitted parameter is load-bearing and assumed rather than derived. The CMB constraint, especially the ISW signal at low ℓ, depends on the perturbation equations: Eq. (4) fixes the background relation, but the likelihood also depends on how the glitch fluid fluctuates. The paper assumes a single perfect fluid with c_s^2 = 1 in the PPF double-field prescription. The motivating theories (cuscuton, Hořava-Lifshitz, Einstein-Aether) have nonstandard sound speeds, anisotropic stress, and in some cases no propagating scalar, so the PPF fluid need not reproduce their linearized dynamics. The c_s^2 ∈ {0.1, 1, 10} check in Section 3 varies one parameter and does not test anisotropic stress or the functional form of the perturbation equations. Please either implement the actual perturbation equations for at least one concrete theory and show that they reduce to the fluid limit, or restrict the interpretation to a phenomenological fluid and do not identify Ω_g with G_cosmo/G_N.
  2. [Section 3.1, Fig. 3] The claimed logarithmic running is not supported by the analysis shown. There are exactly two independent constraints (BBN and CMB) and no fit of a scale-dependent law, no model comparison between constant Ω_g and running Ω_g, and no treatment of the extrapolation to Planck and de Sitter scales. As written, 'logarithmic running' is a speculative narrative, not a result of the paper. Please either add a quantitative fit of the scale dependence with uncertainties or explicitly label these lines as illustrative.
  3. [Section 3.2, Table 2] The 'All' constraint includes the SH0ES distance-ladder measurement, which is the same quantity used to define the Hubble tension the model claims to ease. Including SH0ES can pull Ω_g negative through the Ω_g–H0 degeneracy, so the tightest quoted value (−0.0059 ± 0.0027) is not an independent cosmological constraint. The central CMB+BAO preference is better represented by the Planck18+BAO or PR4+DESI rows; please report those as the primary result and treat the SH0ES-inclusive combination separately.
minor comments (5)
  1. [Figures throughout] The text refers to figures as 'in 1', 'in 3', and 'in 4' without figure numbers; please add the correct figure references.
  2. [Section 3] The prior range on Ω_g is not stated; please specify the uniform prior bounds used in PolyChord, since negative Ω_g regions and phantom-divide crossing can be sensitive to prior volume.
  3. [Section 3.1] The BBN value Ω_g = −0.085 ± 0.027 is taken from Ref. [21] and depends on the EMPRESS 4He measurement; given the active systematics debates around 4He abundances, one sentence noting this would be appropriate.
  4. [Section 3] The paper does not report Δχ² or Bayesian evidence for CGG over ΛCDM; the '2σ preference' would be easier to assess with such a quantity.
  5. [Section 2] The sentence beginning 'It can be rigorously shown...' with Ref. [8] is an important claim; consider spelling out which limits are meant (e.g., weak-field or Vainshtein) since the cited reference is not a standard modified-gravity review.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central Omega_g constraint is an honest fit to external CMB, BAO, supernova, and lensing data, and the reported G_cosmo/G_N is a reparameterization of that fit, not a self-derived prediction.

full rationale

The central constraint on Omega_g is obtained by modifying the CAMB Boltzmann code and sampling the Planck18, PR4, BAO, DES, Pantheon+, and SH0ES likelihoods; it is an honest fit to external data, not an output implied by the model definitions. Equation (4), Omega_g = 1 - G_N/G_cosmo, is a definitional reparameterization: once Omega_g is fitted, reporting G_cosmo/G_N = 0.9914 +/- 0.0045 is algebra, not an independent prediction, and the headline 'weaker superhorizon gravity' is the interpretation of the fitted sign of Omega_g rather than a circular derivation. The PPF treatment with c_s^2 = 1 is an explicit modeling assumption (Section 2), with robustness checks varying c_s^2; it is not an input that already contains the CMB measurement, and a mismatch with the perturbation dynamics of the motivating theories would be an accuracy concern, not circularity. The BBN constraint is imported from the external EMPRESS and Kohri-Maeda analyses; the 'logarithmic running' is a post-hoc interpolation between two independent epochs, not a derivation that presupposes the result. Self-citations ([1], [9], [37]) are contextual or forecast-methodology references and do not carry the load-bearing argument. No step in the derivation chain reduces to its own input by definition.

Assumptions & free parameters 1 free parameters · 5 assumptions · 1 invented entities

The model's only new degree of freedom is Omega_g, fitted to data. The perturbation treatment adds a fluid description with a fixed sound speed. The BBN constraint and the logarithmic running are imported from external measurements and extrapolation, respectively.

free parameters (1)
  • Omega_g (glitch parameter) = -0.0087 ± 0.0046 (Planck18); -0.0059 ± 0.0027 (all data)
    The single new degree of freedom in the model, fitted to CMB and LSS data. It maps to G_cosmo/G_N = 1 - Omega_g via Eq. (4).
assumptions (5)
  • domain assumption Friedmann equation with different gravitational constants on superhorizon and subhorizon scales
    The model is defined by Eq. (1), where H^2 depends on G_cosmo while subhorizon dynamics use G_N. This is the central phenomenological postulate.
  • ad hoc to paper The glitch can be represented as a perfect-fluid dark-energy component with sound speed c_s^2 = 1 (PPF framework)
    Section 2: the CGG component is treated as a perfect fluid at the linear perturbation level and the sound speed is assumed to be 1. This mapping is needed to compute CMB spectra but is not derived from cuscuton, Horava-Lifshitz, or Einstein-Aether theories.
  • domain assumption Standard six-parameter LCDM background with radiation, matter, and cosmological constant
    The baseline model is LCDM with six free parameters; the glitch is added on top. This is stated in Section 2 and used in the likelihood analysis.
  • domain assumption GR is recovered on sub-Hubble scales, so the glitch only affects near- or super-horizon scales
    Stated in Section 1 via Refs. [8,9]: the theories are indistinguishable from GR in asymptotically flat spacetimes, hence only constrained at Hubble scales.
  • domain assumption BBN constraint on Omega_g from EMPRESS helium abundance is taken at face value
    Omega_g = -0.085 ± 0.027 during BBN is imported from Ref. [21] without re-analysis and used to motivate the running in Fig. 3.
invented entities (1)
  • Glitch energy density component (Omega_g rho_crit)
    purpose: An effective dark-energy-like fluid that absorbs the difference between G_cosmo and G_N in the Friedmann equation and is used to evolve perturbations in CAMB.
    It is a bookkeeping device defined by Eq. (4), not a new fundamental field. It has no falsifiable handle beyond the fitted parameter Omega_g itself.

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Pith. "Pith review of A glitch in gravity: cosmic Lorentz-violation from fiery Big Bang to glacial heat death." pith.science (2026). https://pith.science/paper/QBVD6I6O

@misc{pith2026241209568,
  author       = {Pith},
  title        = {Pith review of: A glitch in gravity: cosmic Lorentz-violation from fiery Big Bang to glacial heat death},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QBVD6I6O}},
  note         = {Machine review of arXiv:2412.09568}
}
abstract

One regime where we might see departures from general relativity is at the largest accessible scales, with a natural choice in cosmology being the cosmological horizon (or Hubble) scale. We investigate a single-parameter extension to the standard cosmological model with a different strength of gravity above and below this scale -- a "cosmic glitch" in gravity. Cosmic microwave background observations, and Baryonic Acoustic Oscillations (including the recent DESI Y1) favour weaker superhorizon gravity, at nearly a percent (or 2$\sigma$ level), easing both the Hubble and clustering tensions with other cosmological data. This compounds evidence for an even stronger glitch during Big Bang nucleosynthesis (from helium abundance observations), suggesting that symmetries of general relativity are maximally violated at the Big Bang, but gradually recovered as we approach the present-day cosmological de Sitter scale, associated with the observed dark energy.

Discussion (0). Continue with ORCID to comment.

Forward citations

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  2. Background-level reconstruction of scalar-field potentials from dark-energy histories and comparison with analytic potential families

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