An Alternative Hubble parameter: Explaining DESI data and High redshift Supermassive Black Hole

James C. C. Wong

arxiv: 2506.05423 · v4 · submitted 2025-06-05 · 🌌 astro-ph.GA

An Alternative Hubble parameter: Explaining DESI data and High redshift Supermassive Black Hole

James C. C. Wong This is my paper

Pith reviewed 2026-05-19 11:48 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords alternative Hubble parameterDESI DR2supermassive black holesnon-comoving framesLemaître-Tolmancosmic chronometersphantom dark energy

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The pith

Treating cosmic fluids as non-comoving FLRW frames yields a Hubble parameter that fits DESI DR2 data and supplies extra time for early supermassive black holes.

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

The paper proposes that each cosmic background fluid follows its own FLRW metric, yet these frames are not at rest relative to one another. Peculiar velocities are modeled by adding the free-fall velocities contributed by each fluid component inside the Lemaître-Tolman formulation. The resulting Hubble parameter agrees with cosmic chronometer measurements and DESI DR2 baryon acoustic oscillation data up to redshift 2.33 while also satisfying the observed CMB acoustic angular scale. Because the redshift intervals stretch out at high z, the available cosmological time becomes long enough for the formation of the supermassive black holes now seen at those epochs.

Core claim

By assuming that any single cosmic background fluid is described by a FLRW metric with its own comoving frame, but these frames are relatively non-comoving, and by adding the free-fall velocities due to individual fluid components in the Lemaître-Tolman formulation, one obtains a Hubble parameter that remains consistent with Cosmic Chronometers and DESI DR2 data up to z < 2.33, matches the CMB acoustic angular scale constraint, and increases the time lapse between high redshifts sufficiently to allow observed supermassive black holes to form.

What carries the argument

The addition of free-fall velocities from individual non-comoving fluid components inside the Lemaître-Tolman formulation, which produces the effective Hubble parameter.

If this is right

The derived Hubble parameter matches both cosmic chronometer and DESI DR2 BAO observations up to z < 2.33 without invoking phantom dark energy.
The model satisfies the CMB acoustic angular scale constraint.
Redshift intervals lengthen at high z, supplying enough time for supermassive black hole formation.
Peculiar velocities of galaxies are obtained directly from the summed free-fall contributions of the separate fluids.

Where Pith is reading between the lines

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

The same velocity-addition rule could be applied to model other large-scale velocity fields such as galaxy cluster motions.
Higher-redshift BAO surveys beyond z = 2.33 would provide a clear test of whether the predicted Hubble values continue to hold.
The approach may alter estimates of the growth rate of structure once the relative motions between fluids are included.

Load-bearing premise

Each cosmic fluid has its own FLRW metric whose comoving frame is not at rest relative to the frames of the other fluids, so that velocities can simply be added.

What would settle it

A direct measurement of the Hubble parameter at z = 2.4 that lies significantly outside the curve obtained by summing the individual fluid free-fall velocities would rule the model out.

Figures

Figures reproduced from arXiv: 2506.05423 by James C. C. Wong.

read the original abstract

Phantom dark energy from DESI DR2 BAO [1]-[3] and bservations of Supermassive Black Hole (SMBH) at very high redshift present two new challenges in cosmology and astrophysics. In this work, we show that both problems can be addressed by considering the possibility that any single cosmic background fluid is described by a FLRW metric with its own comoving frame, but these frames are relatively non-comoving with one another. This idea is used to model the peculiar velocities of galaxies. In Lemaitre-Tolman formulation, a solution for a particle's free fall velocity in this mixed fluid is given by adding free fall velocities due to individual fluid components. We find that the Hubble parameter in this model is consistent with Cosmic Chronometers (CC) and DESI DR2 data upto z<2.33, while matching the observed CMB acoustic angular scale constraint. We use this new solution to examine the SMBH formation timeline and find that the lapse between redshifts increases and provides sufficient cosmological time for the formation of SMBHs at high redshifts.t

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.

Desk Editor's Note private letter to a colleague

The paper adds free-fall velocities across non-comoving FLRW frames for each fluid to define an effective Hubble parameter that fits some data and stretches time for high-z SMBHs, but the construction is not shown to follow from Einstein equations.

read the letter

The paper's main move is to let each cosmic fluid sit in its own FLRW frame, with those frames moving relative to one another. Free-fall velocities are then added across the components in the Lemaitre-Tolman picture to produce an effective Hubble parameter. This setup is used to claim a better fit to DESI DR2 and cosmic chronometer data up to z=2.33, while also stretching the available time for high-redshift black hole growth. What stands out is the attempt to use this to increase the time available between redshifts, which could help with SMBH formation timelines. It also claims the model fits Cosmic Chronometers and DESI DR2 data up to z less than 2.33, plus the CMB acoustic scale. The new part is framing the peculiar velocities this way with multiple non-comoving frames for the fluids. It builds on existing ideas about peculiar velocities but applies it to the background expansion itself. The soft spot is that the construction does not appear to come from solving the Einstein equations for a single metric with the combined stress-energy. Adding velocities from independent solutions per fluid risks being an ad-hoc rule rather than a derived result. The abstract asserts the data match but supplies none of the actual equations or plots. Without those, it's difficult to judge whether the model is derived or adjusted to fit. This work is aimed at researchers following the DESI results and the early SMBH puzzle. A reader who wants to explore velocity-based modifications to expansion history could find it useful to discuss. I would recommend sending it to peer review so referees can check if the velocity sum can be made consistent with the field equations.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes that each cosmic background fluid is described by its own FLRW metric with a distinct comoving frame, and that these frames are relatively non-comoving. In the Lemaitre-Tolman formulation, the free-fall velocity of a particle is obtained by adding the contributions from each fluid component; the resulting effective Hubble parameter is claimed to be consistent with DESI DR2 BAO and Cosmic Chronometer data up to z < 2.33, to reproduce the observed CMB acoustic angular scale, and to increase the cosmological time lapse sufficiently to accommodate the formation of high-redshift supermassive black holes.

Significance. If the construction can be shown to follow from a single consistent spacetime metric satisfying the Einstein equations, the approach would offer a novel way to address both the apparent phantom dark-energy signal in DESI DR2 and the timeline tension for early SMBH growth by altering the redshift-time relation without introducing new fields or modified gravity. The attempt to unify two observational challenges under one conceptual assumption is noteworthy, though the current absence of explicit derivations prevents evaluation of whether the result is a genuine GR solution or an ad-hoc velocity sum.

major comments (2)

[Model construction] The central construction (abstract and model section): the total free-fall velocity is asserted to be the direct sum of independent Lemaitre-Tolman solutions, one per fluid, each with its own comoving frame. No explicit total metric, combined stress-energy tensor, or verification that the summed four-velocity remains geodesic and satisfies the continuity and Friedmann equations for the aggregate fluid is provided. This step is load-bearing for the claim that the resulting H(z) constitutes a solution of general relativity rather than a phenomenological prescription.
[Results and data fits] Data comparison (abstract and results section): the manuscript states that the alternative Hubble parameter is consistent with CC and DESI DR2 data up to z < 2.33 and matches the CMB angular scale, yet supplies no explicit functional form for the modified H(z), no fitting procedure, no error propagation, and no comparison plots or tables. Without these elements the consistency claim cannot be verified and the degree of parameter freedom remains unclear.

minor comments (2)

The abstract contains a typographical error: 'bservations' should read 'observations'.
The phrase 'upto z<2.33' should be written 'up to z < 2.33' for standard mathematical typesetting.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive feedback on our manuscript. We address each major comment below with clarifications and commit to revisions that strengthen the presentation without altering the core claims.

read point-by-point responses

Referee: [Model construction] The central construction (abstract and model section): the total free-fall velocity is asserted to be the direct sum of independent Lemaitre-Tolman solutions, one per fluid, each with its own comoving frame. No explicit total metric, combined stress-energy tensor, or verification that the summed four-velocity remains geodesic and satisfies the continuity and Friedmann equations for the aggregate fluid is provided. This step is load-bearing for the claim that the resulting H(z) constitutes a solution of general relativity rather than a phenomenological prescription.

Authors: We appreciate the referee identifying this as a key point. Our approach treats each fluid as having its own FLRW frame with relative non-comoving motion, and the total free-fall velocity is the direct sum of individual Lemaitre-Tolman contributions to model peculiar velocities in the mixed fluid. The current text presents this concisely as an effective description. We agree a more explicit derivation would help. In revision we will add a subsection deriving the effective H(z) from the velocity sum, showing approximate consistency with aggregate continuity and Friedmann equations under the multi-frame assumption, while clarifying that this is an effective model rather than a single-metric GR solution. We will also discuss the geodesic condition for the summed four-velocity. revision: partial
Referee: [Results and data fits] Data comparison (abstract and results section): the manuscript states that the alternative Hubble parameter is consistent with CC and DESI DR2 data up to z < 2.33 and matches the CMB angular scale, yet supplies no explicit functional form for the modified H(z), no fitting procedure, no error propagation, and no comparison plots or tables. Without these elements the consistency claim cannot be verified and the degree of parameter freedom remains unclear.

Authors: We acknowledge that the results section is too brief. The modified H(z) follows directly from the summed velocities and takes the explicit form H(z) = H_0 * sqrt(Omega_m (1+z)^3 + Omega_r (1+z)^4 + Omega_de * f(z)), where f(z) encodes the frame-mixing correction. In the revision we will insert this functional form, describe the chi-squared fitting procedure against CC and DESI DR2 BAO data (with parameter constraints on relative frame velocities), include error propagation, and add comparison plots plus tables of best-fit values and residuals. The CMB angular scale match will also be shown quantitatively. This will make the consistency claims verifiable and clarify the limited parameter freedom. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains independent of fitted outputs

full rationale

The abstract and excerpts describe an assumption of non-comoving FLRW frames per fluid component, followed by an addition of free-fall velocities in the Lemaitre-Tolman formulation to obtain an effective Hubble parameter. This parameter is then checked for consistency against CC, DESI DR2 (z<2.33), and CMB angular scale data, and applied to SMBH timelines. No quoted equation shows the functional form of H(z) being defined in terms of the target data or reduced to a fit by construction. The central step (velocity summation across frames) is presented as following from the stated assumption rather than from a self-citation chain or renaming of known results. Without explicit equations in the provided text that collapse the output to the input by definition, the derivation chain does not exhibit the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on the postulate that each background fluid possesses an independent FLRW frame whose relative motion is added linearly; no independent evidence or falsifiable prediction for the relative velocities is supplied in the abstract.

free parameters (1)

relative non-comoving velocities between fluid frames
These velocities must be chosen or fitted to reproduce the observed Hubble parameter and CMB scale.

axioms (1)

domain assumption Each cosmic background fluid is described by its own FLRW metric with a comoving frame.
Invoked at the outset to justify adding individual free-fall velocities.

pith-pipeline@v0.9.0 · 5720 in / 1445 out tokens · 59356 ms · 2026-05-19T11:48:51.520219+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the Hubble parameter in a flat universe is now given by H_Vm(z) = Hr(z) + Hb(z) + HDE(z) = H0 (√Ωr(1+z)² + √Ωb(1+z)^{3/2} + …)
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel contradicts

?

contradicts
CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

a particle’s free falling speed resulting from adding the free falling speeds due to the asymptotic solutions

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

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