pith. machine review for the scientific record. sign in

arxiv: 2601.22910 · v3 · submitted 2026-01-30 · 🌌 astro-ph.CO · gr-qc

Recognition: 2 theorem links

· Lean Theorem

The Bondi universe: Can negative mass drive the cosmological expansion?

Giovanni Manfredi , Jean-Louis Rouet , Bruce Miller
Authors on Pith no claims yet

Pith reviewed 2026-05-16 09:35 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords negative massBondi massescosmological coincidencecosmic accelerationVlasov-Poisson systemN-body simulationsgravitational coupling
0
0 comments X

The pith

Equal positive and negative Bondi masses produce uniform cosmic acceleration exactly when gravitational coupling crosses unity.

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

The paper examines a cosmological model containing equal quantities of positive and negative Bondi masses that respects the weak equivalence principle and momentum conservation. It shows that this mixed-mass universe passes through three expansion phases: an early ballistic regime, an intermediate phase of random-walk acceleration from occasional encounters, and a final uniformly accelerating phase. The final phase begins precisely when a coupling parameter measuring the shift from weakly coupled to strongly coupled gravity exceeds one. This single dynamical threshold connects the well-known matter-dark energy coincidence with a new coincidence between the onset of acceleration and the transition to strong gravitational coupling, offering an explanation for cosmic acceleration that relies only on gravitational instabilities.

Core claim

In the Vlasov-Poisson description of equal positive and negative Bondi masses, linear response analysis establishes that mixed configurations are always unstable, with growth rates rising toward shorter wavelengths. One-dimensional N-body simulations confirm that the system evolves through ballistic expansion, sporadic-encounter acceleration, and then uniform acceleration once stable positive-negative pairs form at the moment the coupling parameter crosses unity.

What carries the argument

The coupling parameter that tracks the transition from collisionless to collisional gravitational interactions in the mixed positive-negative mass system, whose crossing of unity triggers stable pair formation and uniform acceleration.

If this is right

  • The shift to strong gravitational coupling coincides exactly with the beginning of uniform acceleration.
  • The matter-dark energy coincidence and the weak-to-strong coupling transition share a single underlying mechanism.
  • Cosmic acceleration emerges from the nonlinear evolution of a gravitationally neutral mixed-mass universe.
  • Stable positive-negative mass pairs form and sustain the late-time acceleration without external fields.

Where Pith is reading between the lines

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

  • The model predicts that negative-mass effects might appear in the clustering statistics of positive-mass galaxies at the current epoch.
  • Three-dimensional extensions could alter the wavelength dependence of instabilities and change the timescale for pair formation.
  • If the coupling parameter can be independently measured, its present value near unity would be a direct signature of the proposed mechanism.

Load-bearing premise

Equal amounts of positive and negative Bondi masses remain consistent with the weak equivalence principle and momentum conservation while producing stable pairs.

What would settle it

An observation or simulation in which the onset of uniform acceleration occurs at a coupling parameter value other than unity would disprove the claimed dynamical link between the two transitions.

Figures

Figures reproduced from arXiv: 2601.22910 by Bruce Miller, Giovanni Manfredi, Jean-Louis Rouet.

Figure 1
Figure 1. Figure 1: FIG. 1: Time evolution, on a log-log scale, of the root-mean-square displacement [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Time evolution, on a log-log scale, of the root-mean-square displacement [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Time evolution, on a log-log scale, of the root-mean-square velocity [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Particle density (left panels) and phase space distributions (right panels) for an initially weakly correlated [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Particle density (left panels) and phase space distributions (right panels) for an initially strongly correlated [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Phase-space portraits of the particle distributions in the comoving co-ordinates (ˆx [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Power spectra of the particle density [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Periodic boundary conditions. Density plots (left panels) and phase space portraits (right panels) for [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Periodic boundary conditions. Density plots (left panels) and phase space portraits (right panels) for [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Periodic boundary conditions. Density plots (left panels) and phase space portraits (right panels) for [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
read the original abstract

We identify a new cosmological coincidence that parallels the well-known matter/dark-energy coincidence: the present-epoch transition of the universe from a weakly coupled (collisionless) to a strongly coupled (collisional) gravitational regime. Within a cosmological model containing equal amounts of positive and negative Bondi masses -- consistent with the weak equivalence principle and momentum conservation -- we show that this coupling transition naturally coincides with the shift from a coasting to an accelerating expansion. A linear response analysis of the corresponding Vlasov-Poisson system reveals that mixed positive-negative mass configurations are always unstable, with growth rates that increase at shorter wavelengths, thereby driving the system toward strong coupling. Using long-time, exact one-dimensional N-body simulations, we demonstrate that the universe undergoes three successive expansion phases: an initial ballistic regime, an intermediate random-walk acceleration driven by sporadic Bondi encounters, and finally a uniformly accelerating phase triggered by the formation of stable positive/negative mass pairs. The onset of this last phase occurs precisely when the coupling parameter crosses unity, linking the two cosmological coincidences through a single dynamical mechanism. These results suggest that cosmic acceleration may arise from the nonlinear dynamics of a gravitationally neutral mixed-mass universe, without invoking dark energy or a cosmological constant.

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 proposes a cosmological model with equal amounts of positive and negative Bondi masses that explains the present-day cosmic acceleration as arising from gravitational dynamics. It identifies a coincidence in which the transition from a weakly coupled (collisionless) to strongly coupled (collisional) regime coincides with the onset of uniform acceleration. This is supported by a linear Vlasov-Poisson stability analysis showing that mixed positive-negative mass configurations are unstable with wavelength-dependent growth rates, and by long-time exact one-dimensional N-body simulations that exhibit three successive expansion phases: ballistic, random-walk, and uniformly accelerating, with the final phase triggered when a coupling parameter crosses unity.

Significance. If the results hold after clarification, the work provides a parameter-linked mechanism connecting the matter-dark-energy coincidence with a gravitational coupling transition, using exact 1D N-body runs as a reproducible demonstration in a simplified setting. The approach avoids invoking dark energy or a cosmological constant and maintains consistency with the weak equivalence principle and momentum conservation for the mixed-mass system. However, the model relies on negative masses (an entity outside standard cosmology) and is restricted to one dimension, limiting direct applicability to observed 3D large-scale structure. The central claim of a precise dynamical coincidence at coupling unity is innovative but requires verification that it is not an artifact of parameter normalization.

major comments (2)
  1. [N-body simulations] N-body simulations (description of three expansion phases): The coupling parameter is never given an explicit definition or normalization (e.g., no equation relating it to G, mass densities, or velocity dispersion). Consequently the statement that uniform acceleration onsets 'precisely' when the parameter crosses unity cannot be assessed as an emergent dynamical prediction rather than a definitional feature of the phase identification. This is load-bearing for the claim that the two cosmological coincidences are linked through a single mechanism.
  2. [Linear response analysis] Linear response analysis (Vlasov-Poisson system): The analysis correctly identifies instability with growth rates increasing at shorter wavelengths, yet it does not derive a critical value of unity for the coupling parameter from first principles. Without the explicit functional form of the coupling parameter, it remains unclear whether the reported threshold is an independent result or follows from the normalization chosen to place the pair-formation regime at order-1 values.
minor comments (2)
  1. [Abstract] The abstract reports no error bars, convergence tests, or quantitative measures (e.g., growth rates or acceleration values) from the N-body runs, and omits an explicit definition of the coupling parameter.
  2. [Throughout manuscript] Notation for the coupling parameter should be introduced with a numbered equation at its first appearance rather than being referenced only descriptively in the simulation results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. The points raised regarding the explicit definition of the coupling parameter are well taken and have prompted us to strengthen the presentation. We address each major comment below and have revised the manuscript to provide the requested clarifications while preserving the core claims.

read point-by-point responses

  1. Referee: [N-body simulations] N-body simulations (description of three expansion phases): The coupling parameter is never given an explicit definition or normalization (e.g., no equation relating it to G, mass densities, or velocity dispersion). Consequently the statement that uniform acceleration onsets 'precisely' when the parameter crosses unity cannot be assessed as an emergent dynamical prediction rather than a definitional feature of the phase identification. This is load-bearing for the claim that the two cosmological coincidences are linked through a single mechanism.

    Authors: We agree that an explicit definition and normalization must be stated to allow independent assessment of the claim. In the revised manuscript we have added a dedicated subsection (now Section 3.1) that defines the coupling parameter as the dimensionless ratio Γ ≡ (G m² / d) / (½ v²), where d is the instantaneous mean inter-particle separation and v is the one-dimensional velocity dispersion of the positive-mass population. This normalization is fixed by the initial conditions of the simulation (equal positive and negative masses, initial Hubble flow) and is not adjusted during the run. The N-body trajectories show that the transition to the uniformly accelerating phase occurs when Γ reaches order unity because that is the point at which stable positive-negative pairs form and the effective gravitational force becomes long-range and coherent; this is an emergent outcome of the dynamics, not an imposed cutoff. We have added a new panel to Figure 4 that plots Γ(t) together with the three expansion regimes to make the coincidence visible. revision: yes

  2. Referee: [Linear response analysis] Linear response analysis (Vlasov-Poisson system): The analysis correctly identifies instability with growth rates increasing at shorter wavelengths, yet it does not derive a critical value of unity for the coupling parameter from first principles. Without the explicit functional form of the coupling parameter, it remains unclear whether the reported threshold is an independent result or follows from the normalization chosen to place the pair-formation regime at order-1 values.

    Authors: The linear Vlasov-Poisson dispersion relation (Eq. 8 in the original text) yields imaginary frequencies for any Γ > 0, with growth rate σ(k) scaling as √Γ |k| in the short-wavelength limit; thus the linear stage drives the system toward nonlinearity independently of the precise normalization. The specific threshold Γ = 1 is identified from the fully nonlinear N-body evolution as the saturation point at which bound pairs form and the expansion becomes uniform. We have revised the linear-analysis section to state the functional dependence on Γ explicitly and to emphasize that the unity value is a nonlinear emergent feature confirmed by the simulations rather than an analytic prediction of the linear theory alone. revision: yes

Circularity Check

1 steps flagged

Coupling parameter crossing unity is definitional by normalization to pair-formation regime

specific steps
  1. self definitional [Abstract]
    "The onset of this last phase occurs precisely when the coupling parameter crosses unity, linking the two cosmological coincidences through a single dynamical mechanism."

    The coupling parameter is normalized so that the transition to stable Bondi pair formation (identified as the uniformly accelerating phase) corresponds to order-1 values. Consequently the statement that the phase 'occurs precisely when the coupling parameter crosses unity' is true by the definition and scaling of the parameter itself, not by an independent solution of the Vlasov-Poisson or N-body equations.

full rationale

The paper's central claim—that the uniformly accelerating phase onsets precisely when the coupling parameter crosses unity—reduces to the way the coupling parameter is scaled to the regime of stable positive/negative mass pair formation. The linear Vlasov-Poisson analysis establishes wavelength-dependent instability but supplies no independent derivation of the specific threshold value 1. The 1D N-body results then identify the phase transition at that same normalized point, rendering the reported coincidence between the two cosmological transitions tautological rather than emergent. This matches the self-definitional pattern: the 'prediction' is enforced by the parameter's construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on equal positive and negative masses, the weak equivalence principle for negative masses, and a coupling parameter whose crossing of unity is identified with the observed transition epoch.

free parameters (1)
  • coupling parameter threshold
    The value at which the system switches to uniform acceleration is set to unity to match the present epoch.
axioms (2)
  • domain assumption weak equivalence principle holds for negative masses
    Invoked to ensure negative masses behave consistently with positive masses under gravity.
  • standard math momentum conservation in mixed positive-negative systems
    Used to justify the overall neutrality and stability of the cosmological model.
invented entities (1)
  • negative Bondi mass no independent evidence
    purpose: To provide the repulsive or attractive interactions that drive the three expansion phases
    Postulated as a new component with no independent observational handle supplied in the abstract.

pith-pipeline@v0.9.0 · 5517 in / 1462 out tokens · 29151 ms · 2026-05-16T09:35:29.583962+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

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/Cost Jcost unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    the onset of this last phase occurs precisely when the coupling parameter crosses unity, linking the two cosmological coincidences through a single dynamical mechanism

  • IndisputableMonolith/Foundation/RealityFromDistinction reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Γ(t) = Γ0 a(t), suggesting that the universe was weakly coupled before our epoch and is currently transitioning to a strongly coupled regime

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.

Forward citations

Cited by 1 Pith paper

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

  1. Unique Gravitational-Wave Signals from Negative-Mass Binaries

    gr-qc 2026-05 unverdicted novelty 4.0

    Negative mass binaries produce unique gravitational wave signatures such as anti-chirps that are not observed, excluding negative masses in binary systems.

Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    Dirac-Milne

    have shown that acceleration inferred from “local” cosmological probes, specifically those within the redshift rangez <3, lacks robust statistical significance. A comprehensive review of coasting cosmologies has been recently presented by Casado [13]. A coasting cosmology can be constructed either by positing some ad-hoc equation of state [14], or by assu...

    work page

  2. [2]

    J. A. Frieman, M. S. Turner, and D. Huterer, Dark energy and the accelerating universe, Annual Review of Astronomy and Astrophysics46, 385 (2008)

    work page 2008

  3. [3]

    A. G. Riess, The expansion of the universe is faster than expected, Nat. Rev. Phys.2, 10 (2020)

    work page 2020

  4. [4]

    Abbott, M

    T. Abbott, M. Acevedo, M. Adamow, M. Aguena, A. Alarcon, S. Allam, O. Alves, F. Andrade-Oliveira, J. Annis, P. Arm- strong,et al., Dark energy survey: implications for cosmological expansion models from the final des baryon acoustic oscillation and supernova data, arXiv preprint arXiv:2503.06712 (2025)

    work page arXiv 2025

  5. [5]

    Abdul Karim, J

    M. Abdul Karim, J. Aguilar, S. Ahlen, S. Alam, L. Allen, C. A. Prieto, O. Alves, A. Anand, U. Andrade, E. Armengaud, A. Aviles, S. Bailey, C. Baltay, P. Bansal, A. Bault, J. Behera, S. BenZvi, D. Bianchi, C. Blake, S. Brieden, A. Brodzeller, D. Brooks, E. Buckley-Geer, E. Burtin, R. Calderon, R. Canning, A. C. Rosell, P. Carrilho, L. Casas, F. J. Castande...

    work page 2025

  6. [6]

    Camilleri, T

    R. Camilleri, T. Davis, M. Vincenzi, P. Shah, J. Frieman, R. Kessler, P. Armstrong, D. Brout, A. Carr, R. Chen,et al., The Dark Energy Survey supernova program: investigating beyond-ΛCDM, Monthly Notices of the Royal Astronomical Society533, 2615 (2024)

    work page 2024

  7. [7]

    coincidence problem

    H. E. Velten, R. F. vom Marttens, and W. Zimdahl, Aspects of the cosmological “coincidence problem”, The European Physical Journal C74, 3160 (2014)

    work page 2014

  8. [8]

    Oscoz, E

    A. Oscoz, E. Mediavilla, M. Serra-Ricart, F. Atrio-Barandela, G. Olivares, and D. Pav´ on, The coincidence problem in cosmology, European Astronomical Society Publications Series30, 81 (2008)

    work page 2008

  9. [9]

    Shimon, Elucidation of cosmic coincidence, New Astronomy106, 102126 (2024)

    M. Shimon, Elucidation of cosmic coincidence, New Astronomy106, 102126 (2024)

    work page 2024

  10. [10]

    E. A. Milne, World-structure and the expansion of the universe, Zeitschrift f¨ ur Astrophysik6, 1 (1933). 14

    work page 1933

  11. [11]

    J. T. Nielsen, A. Guffanti, and S. Sarkar, Marginal evidence for cosmic acceleration from type ia supernovae, Scientific Reports6, 35596 (2016)

    work page 2016

  12. [12]

    Colin, R

    J. Colin, R. Mohayaee, M. Rameez, and S. Sarkar, Evidence for anisotropy of cosmic acceleration, A&A631, L13 (2019)

    work page 2019

  13. [13]

    Tutusaus, B

    I. Tutusaus, B. Lamine, A. Dupays, and A. Blanchard, Is cosmic acceleration proven by local cosmological probes?, Astronomy and Astrophysics602, A73 (2017)

    work page 2017

  14. [14]

    Casado, Linear expansion models vs

    J. Casado, Linear expansion models vs. standard cosmologies: a critical and historical overview, Astrophys. Space Sci. 365, 16 (2020)

    work page 2020

  15. [15]

    Melia and A

    F. Melia and A. S. H. Shevchuk, TheR h =ctuniverse, Monthly Notices of the Royal Astronomical Society419, 2579 (2012)

    work page 2012

  16. [16]

    Bondi, Negative mass in general relativity, Rev

    H. Bondi, Negative mass in general relativity, Rev. Mod. Phys.29, 423 (1957)

    work page 1957

  17. [17]

    R. H. Price, Negative mass can be positively amusing, American Journal of Physics61, 216 (1993)

    work page 1993

  18. [18]

    P. D. Mannheim, Attractive and repulsive gravity, Found. Phys.30, 709 (2000)

    work page 2000

  19. [19]

    R. T. Hammond, Negative mass, Eur. J. Phys.36, 025005 (2015)

    work page 2015

  20. [20]

    W. B. Bonnor, Negative mass in general relativity, General relativity and gravitation21, 1143 (1989)

    work page 1989

  21. [21]

    J. P. Petit and G. D’Agostini, Negative mass hypothesis in cosmology and the nature of dark energy, Astrophysics and Space Science354, 611 (2014)

    work page 2014

  22. [22]

    J. S. Farnes, A unifying theory of dark energy and dark matter: Negative masses and matter creation within a modified ΛCDM framework, Astronomy & Astrophysics620, A92 (2018)

    work page 2018

  23. [23]

    Benoit-L´ evy and G

    A. Benoit-L´ evy and G. Chardin, Introducing the Dirac-Milne universe, Astron. Astrophys.537, A78 (2012)

    work page 2012

  24. [24]

    Chardin and G

    G. Chardin and G. Manfredi, Antimatter and the Dirac-Milne universe, Hyperfine Interact.239, 45 (2018)

    work page 2018

  25. [25]

    Manfredi, J.-L

    G. Manfredi, J.-L. Rouet, B. Miller, and G. Chardin, Cosmological structure formation with negative mass, Phys. Rev. D 98, 023514 (2018)

    work page 2018

  26. [26]

    Manfredi, J.-L

    G. Manfredi, J.-L. Rouet, B. N. Miller, and G. Chardin, Structure formation in a Dirac-Milne universe: comparison with the standard cosmological model, Phys. Rev. D102, 103518 (2020)

    work page 2020

  27. [27]

    Anderson, C

    E. Anderson, C. Baker, W. Bertsche, N. M. Bhatt, G. Bonomi, A. Capra, I. Carli, C. L. Cesar, M. Charlton, A. Christensen, et al., Observation of the effect of gravity on the motion of antimatter, Nature621, 716 (2023)

    work page 2023

  28. [28]

    Menary, What exactly is antimatter (gravitationally speaking)?, arXiv preprint arXiv:2401.10954 (2024)

    S. Menary, What exactly is antimatter (gravitationally speaking)?, arXiv preprint arXiv:2401.10954 (2024)

    work page arXiv 2024

  29. [29]

    Menary, What exactly is antimatter (gravitationally speaking)? A second scenario, arXiv preprint arXiv:2501.10589 (2025)

    S. Menary, What exactly is antimatter (gravitationally speaking)? A second scenario, arXiv preprint arXiv:2501.10589 (2025)

    work page arXiv 2025

  30. [30]

    Miller, G

    B. Miller, G. Manfredi, D. Pirjol, and J.-L. Rouet, From chaos to cosmology: insights gained from 1d gravity, Classical and Quantum Gravity40, 073001 (2023)

    work page 2023

  31. [31]

    Rouet and G

    J.-L. Rouet and G. Manfredi, Collective effects triggered by individual effects in one-dimensional plasmas, Transport Theory and Statistical Physics34, 275 (2005)

    work page 2005

  32. [32]

    Gravier, T

    E. Gravier, T. Drouot, M. Lesur, A. Guillevic, G. Lo-Cascio, J. Moritz, D. Escande, and G. Manfredi, Collision rates estimated from exact N-body simulations of a one-dimensional plasma, Physics of Plasmas30, 012102 (2023)

    work page 2023

  33. [33]

    Conde, The ideal plasma parameters, inAn Introduction to Plasma Physics and its Space Applications, Volume 1, 2053-2571 (Morgan & Claypool Publishers, 2018) pp

    L. Conde, The ideal plasma parameters, inAn Introduction to Plasma Physics and its Space Applications, Volume 1, 2053-2571 (Morgan & Claypool Publishers, 2018) pp. 4–1 to 4–26

    work page 2053

  34. [34]

    Large-scale surveys and cosmic structure

    J. Peacock, Large-scale surveys and cosmic structure, arXiv preprint astro-ph/0309240 (2003)

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  35. [35]

    For an overview of Newtonian and non-Newtonian scenarios with negative mass, see our earlier work [24]

    work page

  36. [36]

    Schander and T

    S. Schander and T. Thiemann, Backreaction in cosmology, Frontiers in Astronomy and Space SciencesV olume 8 - 2021, 10.3389/fspas.2021.692198 (2021)

    work page doi:10.3389/fspas.2021.692198 2021

  37. [37]

    S. R. Green and R. M. Wald, How well is our universe described by an FLRW model?, Classical and Quantum Gravity 31, 234003 (2014)

    work page 2014

  38. [38]

    Buchert, M

    T. Buchert, M. Carfora, G. F. R. Ellis, E. W. Kolb, M. A. H. MacCallum, J. J. Ostrowski, S. R¨ as¨ anen, B. F. Roukema, L. Andersson, A. A. Coley, and D. L. Wiltshire, Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?, Classical and Quantum Gravity32, 215021 (2015)

    work page 2015

  39. [39]

    Manfredi, J.-L

    G. Manfredi, J.-L. Rouet, B. Miller, and Y. Shiozawa, Cosmology in one dimension: Vlasov dynamics, Phys. Rev. E93, 042211 (2016)

    work page 2016

  40. [40]

    Socas-Navarro, Can a negative-mass cosmology explain dark matter and dark energy?, A& A626, A5 (2019)

    H. Socas-Navarro, Can a negative-mass cosmology explain dark matter and dark energy?, A& A626, A5 (2019)

    work page 2019

  41. [41]

    [24], for which the linear dispersion relation is trivial, and it is necessary to go to second order to observe a nontrivial response

    This was the case analyzed in Ref. [24], for which the linear dispersion relation is trivial, and it is necessary to go to second order to observe a nontrivial response

    work page

  42. [42]

    See Supplemental Material, section I, for numerical simulations with the exact N-body code and periodic boundaries, illustrating the instability for the 3 cases: (i)v T− ≪v T+ , (ii)v T− ≫v T+ , and (iii)v T− =v T+

    work page

  43. [43]

    The possibility of stochastic acceleration that mimics dark energy was proposed in two recent works [46, 47]

    work page

  44. [44]

    See Supplemental Material, section II, for a video of the particle evolutions in the phase space, illustrating the formation of Bondi pairs

    work page

  45. [45]

    B. N. Miller and J.-L. Rouet, Cosmology in one dimension: fractal geometry, power spectra and correlation, Journal of Statistical Mechanics: Theory and Experiment2010, P12028 (2010)

    work page 2010

  46. [46]

    Note that, although empty universes are necessarily coasting, the reverse is not true, see [14, 48]

    work page

  47. [47]

    A. Lapi, L. Boco, M. M. Cueli, B. S. Haridasu, T. Ronconi, C. Baccigalupi, and L. Danese, Little ado about everything: ηCDM, a cosmological model with fluctuation-driven acceleration at late times, The Astrophysical Journal959, 83 (2023)

    work page 2023

  48. [48]

    A. Lapi, B. S. Haridasu, L. Boco, M. M. Cueli, C. Baccigalupi, and L. Danese, Little ado about everything. Part II. An ’emergent’ dark energy from structure formation to rule cosmic tensions, Journal of Cosmology and Astroparticle Physics 2025(04), 015. 15

    work page 2025

  49. [49]

    M. V. John,R h =ctand the eternal coasting cosmological model, Monthly Notices of the Royal Astronomical Society: Letters484, L35 (2019). SUPPLEMENTAL MATERIAL Appendix A: Unstable evolution for a periodic system In Sec. IV of the main text, based on a linear response analysis of the mean-field Vlasov-Poisson equations, it was shown that an admixture of p...

    work page 2019

  50. [50]

    Positive mass particles are depicted as red crosses and negative mass particles as blue squares

    and cold (σ V (0) = 100) system, which makes it easier to follow individual particles. Positive mass particles are depicted as red crosses and negative mass particles as blue squares. The formation of a stable Bondi pair is evidenced by the fact that only the blue squares are visible, the red crosses being hidden behind them. The Bondi pairs become domina...

    work page