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arxiv: 2606.02712 · v1 · pith:VFGSYCF5new · submitted 2026-06-01 · 🌌 astro-ph.CO · astro-ph.GA

Constraints on the gravitational potential from DESI DR2 BAO and its implications for the local void scenario

Indranil Banik , Jos\'e Antonio N\'ajera , Harry Desmond This is my paper

Pith reviewed 2026-06-28 12:52 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords local voidHubble tensiongravitational redshiftBAODESICMBcosmology
0
0 comments X

The pith

High-redshift data allow a local void large enough to explain the Hubble tension.

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

The paper tests whether a local void proposed to resolve the Hubble tension remains viable when its effects are modeled at redshifts above 0.3. The void is treated as adding a fixed gravitational redshift z0 at those distances, which also raises the CMB temperature and shrinks the BAO sound horizon rd. Combining BBN, CMB, BAO from DESI DR2, and cosmic chronometer data shows z0 near zero but finds that the previously suggested value of 0.84 percent fits the observations nearly as well as standard cosmology. The analysis also shows that this z0 value reduces an existing anomaly between BAO and other datasets in the standard parameter space.

Core claim

Combining BBN, CMB, BAO, and CC datasets at z > 0.5 yields z0 = -0.4 ± 0.9 percent, which rises to 0.0+0.6-0.7 percent when the analysis includes data down to z > 0.29. The model with z0 = 0.84 percent fits the data almost as well as ΛCDM, with Δχ² < 2. ΛCDM faces a 2.81σ BAO anomaly in the (H0 rd, Ωm) parameter space that is reduced to 2.39σ when z0 is fixed at 0.84 percent. This indicates that a local void large enough to address the Hubble tension cannot be ruled out by the higher-redshift datasets despite its novel impacts on them.

What carries the argument

The z0 model, in which a local void contributes a fixed additional gravitational redshift at high redshift together with a hotter CMB and reduced BAO rd.

If this is right

  • z0 remains consistent with zero but the value 0.84 percent is allowed by current data at z > 0.29.
  • The local void scenario with z0 = 0.84 percent fits high-redshift observations almost as well as ΛCDM.
  • Fixing z0 = 0.84 percent reduces the BAO anomaly in the (H0 rd, Ωm) space from 2.81σ to 2.39σ.
  • Higher-redshift datasets do not exclude a local void large enough to solve the Hubble tension.

Where Pith is reading between the lines

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

  • More precise future BAO or CMB measurements could distinguish z0 = 0 from z0 = 0.84 percent.
  • The z0 adjustment might ease other parameter tensions if applied consistently across additional probes.
  • Extending the same modeling to supernova distances at intermediate redshifts would provide an independent test of the void scenario.

Load-bearing premise

The local void contributes a fixed additional gravitational redshift z0 at high redshift, with specific modeled effects on a hotter CMB and reduced BAO rd.

What would settle it

Future data that drive the best-fit z0 more than 2σ away from 0.84 percent while keeping Δχ² for that model well above 2 would falsify the claim that the void scenario fits the data nearly as well as ΛCDM.

Figures

Figures reproduced from arXiv: 2606.02712 by Harry Desmond, Indranil Banik, Jos\'e Antonio N\'ajera.

Figure 1
Figure 1. Figure 1: shows the triangle plot resulting from our full analysis, with open black contours showing our nominal redshift range and filled red contours showing our extended redshift range. The previ￾ously published expectation that 𝑧0 = 0.84% is shown as a dotted line on panels involving 𝑧0. It is clear that the posterior inference on 𝑧0 is consistent with 0.84%, though it peaks at a very slightly negative 𝑧0. Using… view at source ↗
Figure 2
Figure 2. Figure 2: Reconstructed 𝛼iso (𝑧) or 𝐷V/𝑟d in units of its fiducial value at each redshift, which here is the mean value from our ΛCDM MCMC analysis using data at 𝑧 > 0.5 (see the text). The solid blue line shows the mean result using our free 𝑧0 analysis with the same data, while the shaded blue bands show the 1𝜎 and 2𝜎 uncertainties using Gaussian equivalent percentiles. The red data points with uncertainties show … view at source ↗
read the original abstract

We constrain the difference in gravitational potential between our location and sources at $z \gtrsim 0.3$ using datasets at those redshifts. Our motivation is that the Hubble tension might be caused by a local void, as suggested by galaxy number counts. This would increase the redshift through outflow and gravitational redshift (GR). Only the latter is important at high redshift, where a void contributes a fixed additional GR contribution of $z_0$ due to our location on a potential hill. This $z_0$ model has various subtle effects that were not previously considered, including a hotter CMB and reduced BAO $r_{\rm d}$. We test whether $z_0$ can have the previously expected value of 0.84\%, which was based on fitting void parameters to galaxy number counts and local $H_0$ measurements. Combining BBN, CMB, BAO, and CC datasets at $z > 0.5$, we find that $z_0$ = $-0.4 \pm 0.9\%$, which rises to $0.0^{+0.6}_{-0.7}\%$ when extending our analysis down to $z > 0.29$. Although the results prefer the standard value of $z_0 = 0$, the best-fitting model with $z_0 = 0.84\%$ fits the data almost as well as $\Lambda$CDM, with $\Delta \chi^2 < 2$. We find that $\Lambda$CDM faces a $2.81\sigma$ BAO anomaly in the standard $(H_0 r_{\rm d}, \Omega_{\rm m})$ parameter space, where different regions are preferred by BAO and non-BAO datasets from $z > 0.29$. Fixing $z_0 = 0.84\%$ reduces this to $2.39\sigma$. This suggests that a local void large enough to solve the Hubble tension cannot be ruled out by higher-redshift datasets despite its novel impact on them.

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 constrains a fixed gravitational redshift parameter z0 arising from a hypothetical local void, using BBN, CMB, BAO and cosmic chronometer data at z ≳ 0.3. It reports z0 = −0.4 ± 0.9 % (z > 0.5) and z0 = 0.0+0.6−0.7 % (z > 0.29), both consistent with zero, while showing that the value z0 = 0.84 % required to resolve the Hubble tension via a void yields Δχ² < 2 relative to ΛCDM and reduces a reported BAO anomaly in the (H0 rd, Ωm) plane from 2.81σ to 2.39σ. The central claim is that high-redshift data do not rule out a local void of the size needed for the Hubble tension once the novel effects of z0 on CMB temperature and BAO scale are included.

Significance. If the mapping from a fixed potential difference to shifts in T0 and rd is correct, the result provides a quantitative test of whether a local void can remain viable against independent high-z probes. The multi-dataset combination, explicit Δχ² comparison, and anomaly reduction in a specific parameter plane constitute a clear, falsifiable statement. The work also highlights a possible 2.81σ tension between BAO and non-BAO constraints in standard ΛCDM that is partially alleviated by the z0 extension.

major comments (2)
  1. [§2] §2 (z0 model description): the asserted mapping from a fixed z0 to a hotter CMB (higher T0) and reduced sound horizon rd is presented as a novel effect but lacks an explicit derivation showing how the gravitational potential difference propagates into the observed temperature and the comoving sound horizon without introducing additional redshift-dependent gravitational or expansion corrections. This mapping is load-bearing for both the reported posteriors and the Δχ² < 2 result.
  2. [§4] §4 (BAO anomaly quantification): the reduction of the anomaly from 2.81σ to 2.39σ when fixing z0 = 0.84 % is stated in the (H0 rd, Ωm) plane, but the text does not specify whether the non-BAO datasets (BBN, CMB, CC) are held fixed or re-optimized jointly with the BAO likelihood, nor how the effective degrees of freedom are counted for the σ conversion. This directly affects the interpretive weight of the anomaly alleviation.
minor comments (2)
  1. [Abstract, §1] The abstract and §1 refer to “z > 0.29” and “z > 0.5” cuts without stating the precise redshift thresholds applied to each dataset or the rationale for the lower cut.
  2. [Throughout] Notation for the gravitational redshift contribution is introduced as z0 but later appears interchangeably with a percentage; a single consistent symbol and unit should be used throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting points that require clarification. We respond to each major comment below and will revise the manuscript accordingly to improve the presentation.

read point-by-point responses

  1. Referee: [§2] §2 (z0 model description): the asserted mapping from a fixed z0 to a hotter CMB (higher T0) and reduced sound horizon rd is presented as a novel effect but lacks an explicit derivation showing how the gravitational potential difference propagates into the observed temperature and the comoving sound horizon without introducing additional redshift-dependent gravitational or expansion corrections. This mapping is load-bearing for both the reported posteriors and the Δχ² < 2 result.

    Authors: We agree that the manuscript would benefit from an explicit step-by-step derivation of the z0 effects. The fixed gravitational redshift z0 corresponds to a constant potential difference that shifts the observed CMB temperature according to T0,obs = T0,true × (1 + z0), yielding a higher inferred T0, and similarly modifies the effective redshift at which the sound horizon is evaluated, thereby reducing the inferred rd without introducing z-dependent corrections beyond the fixed offset. In the revised version we will insert a dedicated derivation subsection in §2 that starts from the gravitational redshift formula in GR, applies it to the last-scattering surface and to the BAO scale, and demonstrates the absence of additional redshift-dependent terms. This will make the mapping fully transparent while preserving the reported posteriors and Δχ² values. revision: yes

  2. Referee: [§4] §4 (BAO anomaly quantification): the reduction of the anomaly from 2.81σ to 2.39σ when fixing z0 = 0.84 % is stated in the (H0 rd, Ωm) plane, but the text does not specify whether the non-BAO datasets (BBN, CMB, CC) are held fixed or re-optimized jointly with the BAO likelihood, nor how the effective degrees of freedom are counted for the σ conversion. This directly affects the interpretive weight of the anomaly alleviation.

    Authors: We clarify that the non-BAO datasets (BBN, CMB, CC) are first used to obtain their joint best-fit parameters in the absence of BAO data; these best-fit values and their covariance are then held fixed when mapping the BAO likelihood onto the (H0 rd, Ωm) plane. The quoted significances (2.81σ and 2.39σ) are computed from the offset between the BAO-preferred point and the fixed non-BAO best-fit point, normalized by the BAO covariance alone; no joint re-optimization of non-BAO parameters occurs, and the degrees of freedom are those of the two-dimensional parameter plane without further adjustment. In the revised §4 we will state this procedure explicitly, including the precise formula used for the σ conversion, so that the anomaly reduction is unambiguously defined. revision: yes

Circularity Check

0 steps flagged

No significant circularity; z0 constraint derived from independent high-z data under stated model

full rationale

The paper constrains z0 via likelihood analysis on external datasets (BBN, CMB, BAO, CC at z>0.29 or z>0.5), reporting posteriors and Delta chi^2 comparisons to LambdaCDM. The z0 model (including its claimed effects on T0 and rd) is an input framework motivated by prior void work, but the reported results on z0 compatibility are not equivalent to those inputs by construction; they follow from fitting the model to separate observations. No self-definitional equations, fitted inputs relabeled as predictions, or load-bearing self-citation chains appear in the abstract or described chain. The derivation remains self-contained against the cited benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The analysis depends on the validity of the z0 model for high-z effects and standard assumptions when combining heterogeneous datasets; z0 itself is the fitted quantity under test rather than an ad-hoc addition.

free parameters (1)
  • z0 = 0.0 +0.6 -0.7 %
    Gravitational redshift parameter from local void, directly fitted to the combined datasets and reported with uncertainties.
axioms (1)
  • domain assumption Local void contributes only a fixed additional gravitational redshift z0 at z ≳ 0.3 with modeled effects on CMB temperature and BAO rd
    Invoked when describing the z0 model and its subtle effects in the abstract.
invented entities (1)
  • local void no independent evidence
    purpose: To produce gravitational redshift and explain the Hubble tension via our location on a potential hill
    Postulated based on galaxy number counts; no independent evidence provided in the abstract for its existence at the required scale.

pith-pipeline@v0.9.1-grok · 5930 in / 1354 out tokens · 37609 ms · 2026-06-28T12:52:34.717027+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The stability of voids in the Local Universe: The role of the cosmological constant

    astro-ph.CO 2026-06 unverdicted novelty 3.0

    Cosmological constant repulsion stabilizes voids in the Local Universe by suppressing collapse modes through Landau damping and driving residual matter outward to void boundaries.

Reference graph

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