Observational Quantities in Quasi-Newtonian Descriptions of Cosmological Space-Times

Asta Heinesen; Davide Fontana; Timothy Clifton

arxiv: 2604.08119 · v1 · submitted 2026-04-09 · 🌀 gr-qc · astro-ph.CO

Observational Quantities in Quasi-Newtonian Descriptions of Cosmological Space-Times

Asta Heinesen , Davide Fontana , Timothy Clifton This is my paper

Pith reviewed 2026-05-10 17:25 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.CO

keywords quasi-Newtonian cosmologyshear-free foliationdistance measuresredshiftlight propagationinhomogeneous modelsFriedmann cosmologycosmological tensions

0 comments

The pith

Quasi-Newtonian space-times let observers calculate distances and redshifts using Newtonian-like quantities even when structures are fully relativistic.

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

The paper establishes that cosmological space-times admitting a shear-free foliation, termed quasi-Newtonian, expand isotropically and reduce small-scale gravity to a Newtonian limit. Under the conditions that rest-mass density dominates the energy-momentum tensor and matter velocities remain small, the authors derive the basic rules for kinematics and how light travels. A reader would care because this supplies a practical bridge: complex general-relativistic models with non-perturbative features can now be expressed through quantities already familiar from perturbation theory and post-Newtonian expansions. The result is a concrete method to measure how much real observables differ from the predictions of a uniform Friedmann universe.

Core claim

In space-times that admit a shear-free foliation, the kinematic quantities and light-propagation rules can be written in terms of quantities understandable from Newtonian cosmology and post-Newtonian expansions. This formulation lets general-relativistic cosmologies that contain non-perturbative structures be described using the same observational measures of distance and redshift employed in perturbation theory, thereby quantifying departures from Friedmann predictions and recasting features of Lemaître-Tolman-Bondi, Szekeres, and Bianchi models in Newtonian degrees of freedom, as illustrated by the degenerate Kasner solution.

What carries the argument

The shear-free foliation that defines quasi-Newtonian space-times, which enforces isotropic expansion while allowing small-scale gravitational physics to recover a Newtonian limit.

If this is right

Observables in models with non-perturbative structures can be computed from quantities already used in cosmological perturbation theory.
Departures of distance and redshift measurements from Friedmann predictions become quantifiable without solving the full Einstein equations.
Features of Lemaître-Tolman-Bondi, Szekeres, and Bianchi cosmologies can be re-expressed using Newtonian degrees of freedom.
The approach supplies a route to interpreting current cosmological tensions through controlled departures from uniformity.

Where Pith is reading between the lines

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

Hybrid numerical schemes could evolve large-scale structure under Newtonian gravity while inserting the derived quasi-Newtonian corrections for light propagation at each step.
The same framework might be used to test whether apparent Hubble-constant discrepancies arise from averaged inhomogeneities rather than new physics.
Generalization to include non-zero pressure or radiation components would allow the method to address epochs before matter domination.

Load-bearing premise

The energy-momentum tensor is dominated by rest-mass density, the three-velocity of matter is small in the quasi-Newtonian frame, and the space-time admits a shear-free foliation.

What would settle it

Exact integration of null geodesics in an inhomogeneous exact solution such as the Lemaître-Tolman-Bondi metric, compared against the quasi-Newtonian distance-redshift formulas, that produces systematic mismatches larger than the small-velocity approximation permits.

read the original abstract

We investigate measures of distance and redshift in cosmological space-times that admit a shear-free foliation, which we henceforth refer to as `quasi-Newtonian'. Space expands isotropically in this description, and small-scale gravitational physics has a natural Newtonian limit, which makes it ideal for considering the physics of wide classes of cosmological models. By assuming that the energy-momentum tensor is dominated by rest-mass density, and that the 3-velocity of matter is small in the quasi-Newtonian frame, we derive fundamental results for kinematics and light propagation. Our results provide a new way of formulating general-relativistic cosmologies with non-perturbative structures in terms of quantities that can be understood from cosmological perturbation theory and post-Newtonian expansions, and allow us to quantify departures of observables from the predictions of Friedmann cosmology. It thereby provides a route to understanding inherently relativistic space-time structures, such as those that occur in Lema\^{i}tre-Tolman-Bondi, Szekeres solutions, and Bianchi cosmologies in terms of Newtonian degrees of freedom. We illustrate our results using the degenerate Kasner solution as an example, and explain how our approach can be used to provide new insights into the current cosmological tensions.

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

This paper derives redshift and distance measures for shear-free cosmological spacetimes under small-velocity dust assumptions, offering a bridge to perturbative language but with limited validation for the non-perturbative models it targets.

read the letter

This paper's main result is a derivation of redshift and distance formulas for cosmological spacetimes that admit shear-free foliations, assuming dust-like matter with small velocities in that frame. It lets you quantify how much observables deviate from Friedmann predictions in models with non-perturbative structures. The derivations for the kinematics and light propagation are the solid new element. They connect the exact solutions to quantities familiar from perturbation theory and post-Newtonian work. The degenerate Kasner example works as a clear test case and shows the method in action for an anisotropic spacetime. A potential issue is whether the assumptions hold up in the models they discuss. LTB and Bianchi solutions can have zones where matter velocities are not small or where the dust approximation fails locally. The abstract does not include error estimates for the neglected terms, so the claim that this quantifies the full departures rests on how well the frame choice keeps velocities perturbative. If the paper demonstrates that or provides bounds, the limitation is minor; otherwise it narrows the practical scope. Readers working on exact inhomogeneous cosmologies or looking for ways to interpret tensions in expansion rates will find this relevant. It is worth a serious referee because the logic is straightforward and the connection to observables is direct, even if some validation on the approximation range is needed. I would recommend peer review, with the referee asked to examine the applicability to the example models.

Referee Report

2 major / 1 minor

Summary. The paper claims to derive fundamental results for kinematics and light propagation (redshift, distance measures) in cosmological spacetimes admitting shear-free foliations ('quasi-Newtonian' descriptions), under the assumptions that the energy-momentum tensor is dominated by rest-mass density and that matter 3-velocities are small in this frame. It asserts that this provides a new formulation of general-relativistic cosmologies with non-perturbative structures (such as LTB, Szekeres, and Bianchi models) in terms of quantities familiar from cosmological perturbation theory and post-Newtonian expansions, thereby quantifying departures from Friedmann cosmology observables, illustrated via the degenerate Kasner solution.

Significance. If the derivations are sound and the assumptions hold in the regimes of interest, this framework could offer a useful bridge between exact GR solutions and perturbative/post-Newtonian methods, aiding interpretation of relativistic structures and cosmological tensions. The explicit starting assumptions from GR principles and the focus on shear-free foliations with isotropic expansion are strengths for conceptual clarity.

major comments (2)

[Abstract and light propagation derivations] Abstract and the section deriving light propagation: The central claim that the results 'allow us to quantify departures of observables from the predictions of Friedmann cosmology' for inherently relativistic structures such as LTB, Szekeres, and Bianchi models rests on the small 3-velocity and rest-mass domination assumptions. These may fail near shell crossings in LTB or in strongly anisotropic regions of Bianchi models, and the manuscript provides no explicit bounds on neglected terms or verification that a shear-free foliation can keep velocities perturbatively small everywhere, weakening support for the non-perturbative quantification claim.
[Illustration with degenerate Kasner solution] Section illustrating results with the degenerate Kasner solution: The example should include an explicit check or estimate of the magnitude of the neglected velocity terms to confirm that the framework captures the full departures from Friedmann predictions in this anisotropic case.

minor comments (1)

[Kinematics section] The notation distinguishing the quasi-Newtonian frame from standard coordinates could be clarified with an explicit coordinate choice or diagram in the kinematics section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us identify areas for clarification. We respond to each major comment below.

read point-by-point responses

Referee: [Abstract and light propagation derivations] Abstract and the section deriving light propagation: The central claim that the results 'allow us to quantify departures of observables from the predictions of Friedmann cosmology' for inherently relativistic structures such as LTB, Szekeres, and Bianchi models rests on the small 3-velocity and rest-mass domination assumptions. These may fail near shell crossings in LTB or in strongly anisotropic regions of Bianchi models, and the manuscript provides no explicit bounds on neglected terms or verification that a shear-free foliation can keep velocities perturbatively small everywhere, weakening support for the non-perturbative quantification claim.

Authors: We agree that the small 3-velocity and rest-mass domination assumptions are central to the derivations and that they limit the regimes in which the framework applies. The shear-free foliation is chosen by construction to render the expansion isotropic and to align with a frame in which matter velocities remain small in the regions of interest for the models considered. Nevertheless, the original manuscript did not supply explicit bounds on the neglected terms or a detailed verification of the foliation's ability to keep velocities perturbatively small in all cases, such as near shell crossings. In the revised manuscript we will insert a new paragraph in the discussion section that states the order-of-magnitude conditions under which the assumptions hold, provides estimates of the size of the omitted velocity terms, and cites existing results on the existence of shear-free foliations in LTB, Szekeres and Bianchi spacetimes. This addition will make the scope of the non-perturbative quantification explicit. revision: partial
Referee: [Illustration with degenerate Kasner solution] Section illustrating results with the degenerate Kasner solution: The example should include an explicit check or estimate of the magnitude of the neglected velocity terms to confirm that the framework captures the full departures from Friedmann predictions in this anisotropic case.

Authors: We accept the suggestion. The degenerate Kasner solution is used only as a minimal anisotropic illustration. In the revised version we will add an explicit calculation of the 3-velocity measured in the quasi-Newtonian frame together with a numerical estimate of the magnitude of the neglected higher-order terms. Because the Kasner metric is a vacuum solution with power-law scale factors, the velocity remains small away from the initial singularity; the added estimate will confirm that the framework reproduces the leading departures from Friedmann observables in this example. revision: yes

Circularity Check

0 steps flagged

No significant circularity: derivations rest on GR plus explicit assumptions without reduction to fits or self-referential definitions

full rationale

The paper starts from the Einstein equations under the stated assumptions (rest-mass dominated energy-momentum tensor, small 3-velocities in the quasi-Newtonian frame, and existence of a shear-free foliation). It then derives kinematic and light-propagation quantities directly from these. No parameter is fitted to data and then relabeled as a prediction; no central step reduces by construction to a prior result by the same authors; no ansatz is smuggled via self-citation; and the reformulation of LTB/Szekeres/Bianchi models is presented as a change of variables rather than a renaming of an already-known empirical pattern. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The central claim rests on three domain assumptions about matter content, velocities, and foliation properties that are typical in cosmological modeling but must hold for the derivations to apply.

axioms (3)

domain assumption Energy-momentum tensor is dominated by rest-mass density
Explicitly stated in the abstract as a prerequisite for the kinematic and light propagation derivations.
domain assumption 3-velocity of matter is small in the quasi-Newtonian frame
Explicitly stated in the abstract as a prerequisite for the kinematic and light propagation derivations.
domain assumption Space-time admits a shear-free foliation (quasi-Newtonian description)
This is the defining property of the class of models under study, stated at the outset of the abstract.

pith-pipeline@v0.9.0 · 5516 in / 1515 out tokens · 49730 ms · 2026-05-10T17:25:16.803804+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages

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gevolution: a cosmological N-body code based on General Relativity

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[22]

In the realm of the Hubble tension—a review of solutions

Eleonora Di Valentino, Olga Mena, Supriya Pan, Luca Visinelli, Weiqiang Yang, Alessandro Melchiorri, David F Mota, Adam G Riess, and Joseph Silk. In the realm of the Hubble tension—a review of solutions . Class. Quant. Grav. , 38(15):153001, 2021

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Analysing the large-scale bulk flow using cosmicflows4: increasing tension with the standard cosmological model

Richard Watkins et al. Analysing the large-scale bulk flow using cosmicflows4: increasing tension with the standard cosmological model . Monthly Notices of the Royal Astronomical Society , 524(2):1885, 2023

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Galaxy clusters as probes of cosmic isotropy

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[1] [1]

Classical and Quantum Gravity , 35(17):175004, 2018

Eloisa Bentivegna, Timothy Clifton, Jessie Durk, Mikolaj Korzy\' n ski, and Kjell Rosquist Black-hole lattices as cosmological models . Classical and Quantum Gravity , 35(17):175004, 2018

work page 2018

[2] [2]

Hubble diagram dispersion from large-scale structure

Timothy Clifton and Joe Zuntz. Hubble diagram dispersion from large-scale structure . Monthly Notices of the Royal Astronomical Society , 400(4):2185, 2009

work page 2009

[3] [3]

Swiss-cheese models and the Dyer-Roeder approximation

Pierre Fleury. Swiss-cheese models and the Dyer-Roeder approximation . Journal of Cosmology and Astroparticle Physics , 2014(06):054, 2014

work page 2014

[4] [4]

Mikko Lavinto, Syksy R \"a s \"a nen, and Sebastian J. Szybka. Average expansion rate and light propagation in a cosmological Tardis spacetime . Journal of Cosmology and Astroparticle Physics , 2013(12):051, 2013

work page 2013

[5] [5]

Koksbang

Sofie M. Koksbang. Light propagation in Swiss cheese models of random close-packed Szekeres structures: Effects of anisotropy and comparisons with perturbative results . Phys. Rev. D , 95(6):063532, 2017

work page 2017

[6] [6]

Ray tracing and hubble diagrams in post-Newtonian cosmology

Viraj AA Sanghai, Pierre Fleury, and Timothy Clifton. Ray tracing and hubble diagrams in post-Newtonian cosmology . Journal of Cosmology and Astroparticle Physics , 2017(07):028, 2017

work page 2017

[7] [7]

Bias and scatter in the Hubble diagram from cosmological large-scale structure

Julian Adamek, Chris Clarkson, Louis Coates, Ruth Durrer, and Martin Kunz. Bias and scatter in the Hubble diagram from cosmological large-scale structure . Phys. Rev. D , 100(2):021301, 2019

work page 2019

[8] [8]

Macpherson

Hayley J. Macpherson. Cosmological distances with general-relativistic ray tracing: framework and comparison to cosmographic predictions . Journal of Cosmology and Astroparticle Physics , 2023(03):019, 2023

work page 2023

[9] [9]

Henk van Elst and George F. R. Ellis. QuasiNewtonian dust cosmologies . Class. Quant. Grav. , 15(11):3545, 1998

work page 1998

[10] [10]

George F. R. Ellis. Shear free solutions in General Relativity Theory . Gen. Rel. Grav. , 43(12):3253, 2011

work page 2011

[11] [11]

Bulk flows in the local Universe and the importance of relativistic effects

Asta Heinesen. Bulk flows in the local Universe and the importance of relativistic effects . Phys. Rev. D , 108(10):103530, 2023

work page 2023

[12] [12]

Gravitational Lensing from a Spacetime Perspective

Volker Perlick. Gravitational Lensing from a Spacetime Perspective . Living Rev. Relativ. , 7(1):9, 2010

work page 2010

[13] [13]

Dyer and Robert C

Charles C. Dyer and Robert C. Roeder. Observations in locally inhomogeneous cosmological models . The Astrophysical Journal , 189:167, 1974

work page 1974

[14] [14]

Light propagation in arbitrary space-times and the gravitational lens approximation

Stella Seitz, Peter Schneider, and Jurgen Ehlers. Light propagation in arbitrary space-times and the gravitational lens approximation . Class. Quant. Grav. , 11(9):2345, 1994

work page 1994

[15] [15]

A general test of the Copernican principle

Chris Clarkson, Bruce Bassett, and Teresa Hui-Ching Lu. A general test of the Copernican principle . Phys. Rev. Lett. , 101(1):011301, Jul 2008

work page 2008

[16] [16]

Optical drift effects in general relativity

Miko aj Korzy\'nski and Jaros aw Kopi\'nski. Optical drift effects in general relativity . Journal of Cosmology and Astroparticle Physics , 2018(03):012, 2018

work page 2018

[17] [17]

Gravity: Newtonian, post-Newtonian, relativistic

Eric Poisson and Clifford M Will. Gravity: Newtonian, post-Newtonian, relativistic . Cambridge University Press , 2014

work page 2014

[18] [18]

Lema\^ i tre–Tolman–Bondi solutions in the Newtonian gauge: from strong to weak fields

Karel Van Acoleyen. Lema\^ i tre–Tolman–Bondi solutions in the Newtonian gauge: from strong to weak fields . Journal of Cosmology and Astroparticle Physics , 2008(10):028, 2008

work page 2008

[19] [19]

Backreaction in Late-Time Cosmology

Thomas Buchert and Syksy Räsänen. Backreaction in Late-Time Cosmology . Annual Review of Nuclear and Particle Science , 62:57, 2012

work page 2012

[20] [20]

Giblin, James B

John T. Giblin, James B. Mertens, Glenn D. Starkman, and Chi Tian. Limited accuracy of linearized gravity . Phys. Rev. D , 99(2):023527, 2019

work page 2019

[21] [21]

gevolution: a cosmological N-body code based on General Relativity

Julian Adamek, David Daverio, Ruth Durrer, and Martin Kunz. gevolution: a cosmological N-body code based on General Relativity . Journal of Cosmology and Astroparticle Physics , 2016(07):053, 2016

work page 2016

[22] [22]

In the realm of the Hubble tension—a review of solutions

Eleonora Di Valentino, Olga Mena, Supriya Pan, Luca Visinelli, Weiqiang Yang, Alessandro Melchiorri, David F Mota, Adam G Riess, and Joseph Silk. In the realm of the Hubble tension—a review of solutions . Class. Quant. Grav. , 38(15):153001, 2021

work page 2021

[23] [23]

Analysing the large-scale bulk flow using cosmicflows4: increasing tension with the standard cosmological model

Richard Watkins et al. Analysing the large-scale bulk flow using cosmicflows4: increasing tension with the standard cosmological model . Monthly Notices of the Royal Astronomical Society , 524(2):1885, 2023

work page 2023

[24] [24]

A test of the cosmological principle with quasars

Nathan Secrest, Sebastian von Hausegger, Mohamed Rameez, Roya Mohayaee, Subir Sarkar, and Jacques Colin. A test of the cosmological principle with quasars . The Astrophysical Journal Letters 908(2): L51 2021

work page 2021

[25] [25]

Galaxy clusters as probes of cosmic isotropy

Konstantinos Migkas. Galaxy clusters as probes of cosmic isotropy . Philosophical Transactions of the Royal Society A , 383(2290):20240030, 2025

work page 2025

[26] [26]

Averaging inhomogeneous Newtonian cosmologies

Thomas Buchert and J \"u rgen Ehlers. Averaging inhomogeneous Newtonian cosmologies . Astronomy and Astrophysics , 320:1, 1997

work page 1997