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A one-parameter Proca-Nuevo dark energy model fits CMB, BAO and supernova data slightly better than ΛCDM (up to 2.4σ) and lowers the Hubble tension from 5.8σ to about 1.5–2.3σ, but only in the limit where its perturbations are switched off.

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2026-08-03 20:05 UTC pith:YE3CZV5N

load-bearing objection The paper's background-only 'special M' fit gives a plausible but conditional preference over LCDM; the full-perturbation tests on the headline datasets are missing, and the abstract's sigma numbers need rechecking. the 3 major comments →

arxiv 2511.21071 v2 pith:YE3CZV5N submitted 2025-11-26 hep-th astro-ph.COgr-qc

Cosmological tensions in Proca-Nuevo theory

Hsu-Wen Chiang , Claudia de Rham , Sebastian Garcia-Saenz , Xue Zhou This is my paper
classification hep-th astro-ph.COgr-qc
keywords Proca-Nuevodark energyHubble tensioncosmological perturbationsvector-tensor theoryphantom dark energymatter power spectrumBayesian model comparison
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.

This paper argues that a one-parameter subclass of extended Proca-Nuevo (EPN) theory—a vector-tensor dark energy model—matches the combined CMB, BAO and supernova data slightly better than ΛCDM, and eases the Hubble tension. The improvement comes from a phantom-like dark energy component whose density scales as ρ_EPN ∝ H^{2M}, which raises the Hubble constant inferred from early-universe data. However, the preference and tension relief hold only when EPN perturbations are artificially decoupled; with full perturbations included, the model is disfavored against CMB+SDSS data, and natural values of the Proca mass would distort the matter power spectrum. The paper concludes that EPN can be made viable only with a mild tuning (a large Proca mass), and that it does not resolve all tensions—it worsens the matter-density discrepancy.

Core claim

The central discovery is that a 'special M' realization of extended Proca-Nuevo theory, with an effective dark energy density scaling as H^{2M} and with EPN perturbations set to zero, is preferred over ΛCDM at 1.5σ for CMB+BAO and at 2.4σ for CMB+BAO+PPS. In this decoupled limit the Hubble tension drops from 5.8σ to about 2.3σ (with BAO) or 1.5σ (without BAO). The authors further show that the full perturbation theory enhances the effective Newton constant and CMB foreground effects for natural values of the Proca mass, so that matching the observed matter power spectrum requires a large, mildly tuned mass (log10 cm ≳ 4). With full perturbations included, the very special and full special mo

What carries the argument

The central object is the 'special M' model: a one-parameter effective dark energy fluid in EPN theory with ρ_EPN ∝ H^{2M}, obtained from an algebraic constraint on the vector field. The analysis separates background dynamics (a modified Friedmann equation) from perturbations. The perturbation treatment uses a decoupling limit—setting the coefficients ω2, ω3, and ω6 to zero—that reduces the scalar perturbation equations to the ΛCDM form; this step carries the headline result. Stability conditions near the de Sitter fixed point restrict M<0 and select the phantom-like branch.

Load-bearing premise

The paper's main preference and Hubble-tension easing come from the 'special M' analysis that sets the EPN perturbation coefficients to zero, an approximation the authors say breaks down at low redshifts; if that decoupling is not a valid description of the datasets used, the headline result does not follow.

What would settle it

A full-perturbation fit of the special EPN model (with M and cm free in their priors) to the CMB+DESI+PPS dataset: if it yields ΔDIC < 0 relative to ΛCDM and a Hubble-tension reduction below 2σ without requiring cm ≳ 10^4, the paper's claim that perturbations spoil the fit would be falsified; if it yields ΔDIC > 0, the background-only preference is confirmed as approximation-dependent.

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

If this is right

  • A phantom-like vector condensate with ρ_EPN ∝ H^{2M} and M<0 can raise the CMB-inferred Hubble constant without a cosmological constant, easing the Hubble tension.
  • Because the same modified Friedmann equation arises in generalized Proca and other dark energy models, the background-level preference applies to a wider class of theories.
  • The full perturbation theory predicts an enhanced effective Newton constant and a BAO-scale excess in the matter power spectrum; matching full-shape galaxy clustering requires Proca masses about two orders of magnitude above the Hubble scale.
  • The model does not resolve all tensions: it trades the Hubble tension for a larger Ωm0 discrepancy between CMB and supernova data.
  • The M = -1/3 ('very special') model reduces the S8 tension relative to DES Y3 but is disfavored by SDSS full-shape clustering data.

Where Pith is reading between the lines

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

  • The 1.5–2.4σ preference rests on the decoupling approximation that EPN perturbations can be ignored; the authors themselves expect this to break down at low redshift, so a full-perturbation fit to the same datasets could substantially weaken the claim.
  • Because the background is degenerate across theories, the data should be read as evidence for the H^{2M} Friedmann modification, not for EPN specifically; perturbation data are needed to break the degeneracy.
  • A decisive next step would be to run the full-perturbation model against CMB+DESI+PPS; if the ΔDIC turns positive as it does for CMB+SDSS, the claimed preference is an artifact of the decoupling.
  • The required large Proca mass is a consistency condition rather than a no-go; future growth-rate measurements at low redshifts (where the effective Newton constant departs from general relativity) could test the decoupling regime directly.

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 / 3 minor

Summary. The paper studies cosmological constraints on extended Proca-Nuevo (EPN) theory, focusing on the 'special' subclass with an effective dark-energy density scaling as ρ_EPN ∝ H^{2M}. It derives the background dynamics, identifies the 'very special' M=-1/3 model, and presents MCMC fits using Planck PR4 CMB, DESI DR1 BAO, PantheonPlus+SH0ES, and SDSS data. The headline results are that the one-parameter 'special M' model is preferred over ΛCDM at 1.5σ (CMB+DESI) and 2.4σ (CMB+DESI+PPS), and that the Hubble tension is reduced. The paper also analyzes scalar perturbations in the special/full-special models, finding that natural Proca masses produce a large enhancement of G_eff and that matching the matter power spectrum requires very large values of log10 cm.

Significance. If the headline claims were fully established, this would be a useful addition to the dark-energy literature: the background modification is shared by several vector-tensor and braneworld models, and the paper makes a careful attempt to go beyond background fits by including perturbations and stability conditions. The use of current CMB, BAO, and SN data, and the explicit treatment of stability bounds, are strengths. However, the central preference claim is not yet established for the full EPN theory, and the abstract's framing is selective in ways that overstate the model's success.

major comments (3)
  1. [Abstract; Sec. 3; Table 3] The headline preference (1.5σ/2.4σ) is obtained in the 'special M' background-only realization, where EPN perturbations are switched off by setting ω̂2=ω̂3=ω̂6=0 in Eqs. (2.33), reducing the perturbation equations to the ΛCDM form. The paper itself states that this description is expected to break down at low redshifts. In contrast, the full-perturbation 'very special' and 'full special' models are disfavored relative to ΛCDM on CMB+SDSS (ΔDIC=5.28 and 2.22, respectively, Table 3) and require log10 cm ≳ 4–5 to suppress a large G_eff enhancement at natural cm (Fig. 11). Since no full-perturbation fit is presented for CMB+DESI or CMB+DESI+PPS, the abstract's claim that 'the one-parameter Proca-Nuevo model' is preferred is not established for the actual theory; it is established only for a decoupling approximation whose validity on the headline datasets is untested. Please either run the fu
  2. [Sec. 5; Table 4] The abstract presents the reduction of the Hubble tension (from 5.8σ to 2.3/1.5σ) as an 'alleviation' without reporting the accompanying tension budget. The Conclusions state that, for the same M=-1/3 realization, the Ωm0 tension increases from 0.85σ to 5.19σ, 'netting an increase in all tension probes utilized in this work' (Sec. 5). Thus the headline framing is selective: EPN trades an H0 tension for a stronger matter-density tension. The abstract and conclusions should be rewritten to report the net effect, or should explicitly state that H0 is alleviated at the cost of a worsened Ωm0 tension.
  3. [Table 1; Sec. 2.3; Sec. 5] The 'one-parameter' label is used for the model that produces the headline preference, but in the fits M is a free parameter (e.g., posterior M=-0.136^{+0.057}_{-0.051} from CMB+DESI+PPS, Table 2), and in the perturbative realizations log10 cm is also fit with a wide prior (Table 1), while the EFT coefficients are fixed by Eq. (2.43). The model comparison therefore reflects extra fitted freedom, not a one-parameter prediction. Please clarify which realization is being called one-parameter and avoid carrying that label to the full-perturbation EPN model.
minor comments (3)
  1. [Sec. 4.3 / Table 4] The text reports preferences of 1.5σ and 2.4σ, but the conversion from the tabulated ΔDIC/ΔWAIC/ΔlnB values to Gaussian-equivalent σ is not described. Please state the mapping explicitly, and note that different information criteria give somewhat different answers (e.g., Table 4).
  2. [Eq. (2.20); Sec. 2.5] The parameter M is defined with p0 left free, but the perturbation analysis fixes p0=1. The status of p0 and p1 across sections should be stated more consistently to avoid confusion about what is being varied in the fits.
  3. [Table 3; Fig. 4(b)] The log10 cm posteriors for the very special and full special models are irregular, and the table reports lower limits rather than two-sided intervals. Consider reporting a one-sided posterior summary or an explicit statement that the upper limit is not constrained.

Circularity Check

0 steps flagged

No significant circularity: the headline preference is a transparent data fit of a decoupled model, and the cited prior theory is independent of the target tension results.

full rationale

The paper's derivation chain runs from the EPN action (Sec. 2.1) to the background constraint (2.12), the scaling relation rho_EPN ∝ H^{2M} (2.19), the modified Friedmann equation (2.22), and then to linear perturbation equations (2.33) that are implemented in CAMB and fit with Cobaya. The model parameters M and c_m are free parameters constrained by the data; the reported 1.5σ / 2.4σ preference and the H0 shift are posterior outputs from fits to Planck, DESI, PantheonPlus+SH0ES and SDSS data. There is no step in which a target quantity is used to define itself: M is defined through p0 and p1 in Eq. (2.20), not through the preference, and c_m is fitted in the full-perturbation models rather than renamed as a prediction. The background-only 'special M' model is explicitly constructed in Sec. 3 by 'setting ω̂2 = ω̂3 = ω̂6 = 0, ω̂4 = −3M_Pl^2 H^2 and ω̂1 = −2M_Pl^2 H', which 'reduc[es] the perturbation equations back to the ΛCDM set-up.' The paper also discloses the limitation: 'One expects this description to break down at low redshifts.' Thus the headline claim is openly a fit of a decoupled approximation; whether that approximation is valid over the datasets used is a model-validity concern, not a circularity. Self-citations [43, 44, 57, 58] supply the EPN action, the perturbation equations, and previous low-redshift fits. These are prior theoretical/numerical results with stated assumptions that do not include the cosmological-tension conclusion; the paper reproduces the key perturbation equations (2.33)–(2.41) rather than importing the conclusion. No uniqueness theorem from the authors is invoked to forbid alternatives, and the coefficient choice b_i = c_i = −1 is presented as an explicit ansatz, not as a derived prediction. Finally, the information criteria penalize the additional parameters, so the preference is not a fitted input statistically forced by construction. The paper is therefore self-contained against external data benchmarks, and the observed limitations are honestly flagged rather than hidden.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The central claim depends on the EPN action and its coefficient functions, which are chosen from a very general set of free functions (αn, dn). The paper fixes a simple one-parameter subclass by hand, with M and cm fitted to data. The perturbation results additionally require the stability assumptions and the decoupling approximation. No genuinely new particles or forces are introduced beyond the existing EPN vector field.

free parameters (3)
  • M = -0.136 ± 0.057 (CMB+DESI+PPS); ranges [-0.5, 0.5]
    Controls the effective dark-energy scaling ρ_EPN ∝ H^{2M}; fitted to data (Table 2). The phantom-like branch (M<0) is the one preferred by the fits.
  • log10 cm = ≈ 4.4–4.8 (very special and full special models)
    Controls the Proca mass and the coupling of EPN perturbations; large values are required to suppress the effective Newton constant enhancement. Fitted in full perturbation analyses.
  • EFT coefficients b_i, c_i (and e_i through the special-model conditions) = set to -1 (Sec. 2.5)
    Chosen by hand to satisfy stability criteria and simplicity; affects perturbation spectra and Geff. Not fitted but an ad hoc selection within the general EPN parameter space.
axioms (5)
  • domain assumption Positivity of ghost, gradient and tachyon coefficients near the de Sitter fixed point is required
    Used to restrict the parameter space and to justify the 'special' models (Sec. 2.5, Eqs. 2.35–2.41).
  • domain assumption Adiabatic initial conditions suffice for the EPN perturbation system
    Appendix A.1 derives the adiabatic mode and uses it to set CAMB initial conditions; this is assumed to also hold for the four-fluid system in CAMB.
  • ad hoc to paper The decoupling approximation (ω2=ω3=ω6=0) is valid for the dataset combinations where the headline preference is claimed
    The 'special M' background-only realization ignores EPN perturbations, and the paper states the approximation breaks down at low redshift (Sec. 3). This is the load-bearing premise for the 1.5σ/2.4σ preference statements.
  • domain assumption HMcode provides a reliable nonlinear matter power spectrum for EPN models
    Used to compute nonlinear spectra and shown to agree with halofit in random parameter checks (Sec. 3).
  • standard math The vector-field background is homogeneous and time-like, Aμ = −φ(t)dt
    Imposed by FLRW symmetry (Sec. 2.2).

pith-pipeline@v1.3.0-alltime-deepseek · 33095 in / 13920 out tokens · 148656 ms · 2026-08-03T20:05:28.153949+00:00 · methodology

0 comments
read the original abstract

We study the cosmological predictions of (extended) Proca-Nuevo theory. This vector-tensor theory enjoys stable homogeneous and isotropic solutions characterized by an effective dark energy fluid, with behavior that ranges from freezing quintessential to thawing phantom-like, serving as a motivated framework to scrutinize the cosmological tensions that affect the standard $\Lambda$CDM model. While the model we consider is sufficiently generic to encompass a large class of field theories, it distinguishes itself from scalar dark energy models (quintessential ones, kinetic ones and non-minimally coupled ones) by the presence of what would be classed as a vector degree of freedom which can be for instance inherited from more generic theories of gravity. We improve on previous work in several directions: we consider a general one-parameter class of background models; identify a so-called 'special' model and analyze observational constraints taking also into account perturbations and making use of wide up-to-date catalogs of datasets including recently released ones. We find that the one-parameter Proca-Nuevo model is preferred over $\Lambda$CDM at $1.5\sigma$ when fitting CMB and BAO data, and at $2.4\sigma$ when further adding low-redshift data. The Hubble tension is alleviated, dropping from $5.8\sigma$ to $2.3\sigma$ (resp. $1.5\sigma$) between CMB with (and resp. without) BAO data and local measurements. On the other hand, we find that the vector field generically introduces a significant enhancement of the effective Newton constant for natural values of parameters, so that matching the observed matter power spectrum requires a mild amount of tuning to suppress the impact of perturbations. Since, at the background level, Proca-Nuevo is degenerate with other classes of theories, our results are also relevant to a wider range of set-ups including and beyond vector-tensor models.

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Forward citations

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