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arxiv: 2605.30926 · v1 · pith:KIYMWRU6new · submitted 2026-05-29 · 🌌 astro-ph.CO · hep-ph

Matter influence on large-scale scalar dynamics

Philippe Brax This is my paper

Pith reviewed 2026-06-28 21:29 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-ph
keywords scalar fieldsstochastic sourceSchwinger-Keldysh formalismdynamical dark energycosmic Meissner effectscreeningback-reactioncosmology
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The pith

Matter modelled as a stochastic source produces stochastic noise and new interactions that modify the large-scale evolution of light scalar fields.

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

The paper treats local matter structures as a stochastic source coupled to light scalar fields and integrates out their short-distance exchanges. Using the Schwinger-Keldysh formalism yields an effective large-scale theory containing stochastic noise from scale exchanges plus additional interactions that alter the scalars' time evolution. These interactions correct the Klein-Gordon equation and can change the scalar potential in ways that resemble dynamical dark energy. When every substructure is screened the large-scale dynamics are suppressed, producing a cosmic Meissner effect. A sympathetic reader cares because the result shows that small-scale cosmic matter can back-react on and reshape the cosmological behaviour of light scalars.

Core claim

After integrating out the short-distance dynamics of matter modelled as a stochastic source in the Schwinger-Keldysh formalism, the large-distance theory for light scalars includes a stochastic noise corresponding to exchanges between short and large scales and new interactions which can affect the time evolution of light scalars; in particular the resulting corrections to the scalar potential could lead to effects akin to dynamical dark energy, while screening of all substructures suppresses large-scale dynamics and produces a cosmic Meissner effect.

What carries the argument

The Schwinger-Keldysh formalism applied to the effective field theory obtained by integrating out short-distance exchanges between matter (treated as a stochastic source) and light scalars, which generates both stochastic noise and new interactions.

If this is right

  • Corrections to the Klein-Gordon equation arise from the new interactions generated by the integrated-out matter exchanges.
  • These corrections can modify the scalar potential and produce effects similar to dynamical dark energy.
  • Complete screening of all substructures suppresses the large-scale dynamics of the scalars.
  • The suppression is described as a cosmic Meissner effect.

Where Pith is reading between the lines

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

  • Cosmological models of light scalars would need to incorporate back-reaction from the distribution of matter substructures.
  • The effective theory offers a systematic route to include small-scale matter effects in calculations of scalar evolution on cosmic scales.

Load-bearing premise

Matter can be represented as a stochastic source whose short-distance exchanges with the scalar are integrated out without residual ultraviolet sensitivity or back-reaction on the matter itself.

What would settle it

An explicit evaluation of the integrated effective action that produces neither stochastic noise nor corrections to the scalar potential would show that matter does not influence large-scale scalar dynamics in the claimed way.

Figures

Figures reproduced from arXiv: 2605.30926 by Philippe Brax.

Figure 1
Figure 1. Figure 1: FIG. 1: Keldysh contour with an operator inserted at time [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
read the original abstract

Local structures in the Universe can influence the dynamics of light scalar fields when coupled to matter. We focus on light test fields evolving in matter modelled as a stochastic source. We describe the effective field theory for light scalars on large scales after integrating out the short distance dynamics. This is most conveniently performed in the Schwinger-Keldysh formalism where we find that the large distance theory involves a stochastic noise corresponding to the exchanges between short and large scales, and new interactions which can affect the time evolution of light scalars. We exemplify this back-reaction when the coupling between matter and scalars is small leading to corrections to the Klein-Gordon equation of the light scalars on large scales. In particular, the resulting corrections to the scalar potential could lead to effects akin to dynamical dark energy. We also consider the situation where all the substructures of the Universe are screened leading to the suppression of large scale dynamics and a cosmic Meissner effect. This highlights the potentially relevant effects of small scale structures on the cosmological dynamics of light scalar fields.

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 claims that modeling matter as a stochastic source and integrating out short-distance dynamics via the Schwinger-Keldysh formalism yields an effective theory for light scalars on large scales. This effective theory includes stochastic noise from scale exchanges and new interactions that modify the Klein-Gordon equation, producing corrections to the scalar potential that can resemble dynamical dark energy. In the fully screened limit, large-scale dynamics are suppressed, resulting in a cosmic Meissner effect.

Significance. If the integration procedure is free of cutoff artifacts and back-reaction issues, the work would demonstrate a concrete channel through which sub-horizon matter structures can influence the late-time evolution of light scalars, potentially linking small-scale clustering to apparent dark-energy behavior without additional fields. The systematic application of the Schwinger-Keldysh contour to derive both noise and induced interactions is a methodological strength that could be extended to other coupled systems.

major comments (2)
  1. [Schwinger-Keldysh integration and effective potential derivation] The central claim that the integrated corrections produce a potential shift 'akin to dynamical dark energy' (abstract and the paragraph following the SK construction) rests on the assumption that the stochastic source yields local, cutoff-independent operators after integration. No explicit demonstration is given that the matter two-point function or higher correlators do not generate non-local or divergent terms that survive the separation between short and large scales; if such terms remain, the effective potential depends on the arbitrary cutoff and the dark-energy analogy is not robust.
  2. [Screened limit discussion] The screened 'cosmic Meissner effect' (final paragraph) is presented as a qualitative suppression of large-scale dynamics, yet the manuscript provides neither the screening length scale nor the resulting modification to the scalar propagator or power spectrum. Without these, it is impossible to assess whether the effect is observationally distinguishable from standard screening mechanisms or consistent with existing bounds on scalar fifth forces.
minor comments (2)
  1. [Abstract] The abstract introduces the 'cosmic Meissner effect' without a brief parenthetical definition or reference to the analogy being drawn; a short clarifying phrase would improve accessibility.
  2. [Effective field theory section] Notation for the stochastic noise correlator and the induced interaction vertices is not introduced until after the SK contour is invoked; defining these symbols at first appearance would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive major comments. We respond to each point below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: The central claim that the integrated corrections produce a potential shift 'akin to dynamical dark energy' (abstract and the paragraph following the SK construction) rests on the assumption that the stochastic source yields local, cutoff-independent operators after integration. No explicit demonstration is given that the matter two-point function or higher correlators do not generate non-local or divergent terms that survive the separation between short and large scales; if such terms remain, the effective potential depends on the arbitrary cutoff and the dark-energy analogy is not robust.

    Authors: We agree that the manuscript does not contain an explicit calculation demonstrating that the integrated matter correlators produce strictly local, cutoff-independent operators in the effective potential. This omission weakens the robustness of the dynamical dark energy analogy. In the revised manuscript we will add a dedicated appendix deriving the leading correction from the matter two-point function on the Schwinger-Keldysh contour, showing that non-local contributions are suppressed by the short-distance cutoff and that any residual divergences are absorbed into a finite renormalization of the scalar mass and self-coupling, leaving the physical effective potential independent of the arbitrary scale separation. revision: yes

  2. Referee: The screened 'cosmic Meissner effect' (final paragraph) is presented as a qualitative suppression of large-scale dynamics, yet the manuscript provides neither the screening length scale nor the resulting modification to the scalar propagator or power spectrum. Without these, it is impossible to assess whether the effect is observationally distinguishable from standard screening mechanisms or consistent with existing bounds on scalar fifth forces.

    Authors: The cosmic Meissner effect is introduced as a limiting-case illustration rather than a quantitative prediction. The manuscript therefore supplies neither an explicit screening length nor the modified propagator. We will revise the final section to state explicitly that the discussion remains qualitative, to indicate how a screening length could be estimated once a concrete screening mechanism is specified, and to note that a comparison with fifth-force bounds lies outside the present scope. This clarification will be added without introducing new quantitative claims. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation uses standard SK integration on stochastic source

full rationale

The paper constructs an EFT for light scalars by integrating short-distance matter dynamics via the Schwinger-Keldysh formalism, yielding stochastic noise and potential corrections as outputs of that procedure. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided text. The central claim (corrections akin to dynamical dark energy) follows from the integration ansatz rather than presupposing the result. This is the expected non-circular outcome for a first-principles EFT derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the Schwinger-Keldysh integration of short-distance matter fluctuations into a stochastic large-scale theory; no explicit free parameters, new entities, or ad-hoc axioms are named in the abstract.

axioms (1)
  • domain assumption Short-distance matter dynamics can be integrated out to yield a well-defined stochastic effective theory for the light scalar on large scales.
    Stated as the starting point for the EFT construction in the abstract.

pith-pipeline@v0.9.1-grok · 5693 in / 1253 out tokens · 20391 ms · 2026-06-28T21:29:56.700290+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

57 extracted references · 20 linked inside Pith

  1. [1]

    At lowest order, the scalar perturbations on large scales obey the linear response theory

    and a novel way of tackling the coincidence problem. At lowest order, the scalar perturbations on large scales obey the linear response theory. On the other hand, when all the structures of the 3 Universe are screened, the resulting dynamics on large scales are tightly determined to be that of a rapidly oscillating scalar at the background level and suppr...

  2. [2]

    This is useful as an illustration compared to the full complexity of the matter power spectrum deduced from the growth of cosmological perturbations

    Time-local and translation invariant processes A simplifying and unrealistic assumption corresponds to taking that time and space translation invariance are respected by the matter distribution. This is useful as an illustration compared to the full complexity of the matter power spectrum deduced from the growth of cosmological perturbations. This hypothe...

  3. [3]

    In this context, ⃗kis just the usual comoving wavevector

    The cosmological spectrum In the cosmological case that we consider here, we work in comoving coordinates in a spatially flat FRW universe. In this context, ⃗kis just the usual comoving wavevector. We normalise the scale factor toa(t 0) = 1 today, andP( ⃗k, t) should be understood as the matter power spectrum in these comoving coordinates at a given timet...

  4. [4]

    The unscreened case When no screening takes place, i.e. the local structures act only as perturbative corrections to the large scale dynamics, the cosmological field penetrates inside the local structures and serves as a background field everywhere in the Universe. This is a situation where the influence of the local matter density on the dynamics of the ...

  5. [5]

    Screening takes places when the Compton wavelength of the scalar field is much shorter than the size of the local matter over-densities

    Screening When screening takes place locally, the short distance field is determined by the local matter density. Screening takes places when the Compton wavelength of the scalar field is much shorter than the size of the local matter over-densities. The field thus settles at the minimum of the effective potential and satisfies j>B′(¯Φ) +V ′(¯Φ) = 0.(60) ...

  6. [6]

    Unscreened short scales In the unscreened case, we can expand around the cosmological field and get Γ = X n≥0 Γ(n) (72) in powers of ¯Φ. We have for the leading term Γ(0)(ϕ+, ϕ−, ¯Φ) =− Z d4x√−g(∂ϕ −∂ϕ+ + V(ϕ + + ϕ− 2 )−V(ϕ + − ϕ− 2 ) + ¯J(B(ϕ + + ϕ− 2 )−B(ϕ + − ϕ− 2 ))) (73) and the corrections are given by Γ(n)(ϕ+, ϕ−, ¯Φ) =− Z d4x√−g( β mPl )n ¯Φn n! (...

  7. [7]

    This implies that A(L) =− iβ mPl Z |⃗ p|≥1 L /d3p P(⃗ p, ω(p))−P(⃗ p,−ω(p)) 2ω(p) (81) which depends onL

    The correction to the Klein-Gordon equation: unscreened case Let us evaluate the coefficient of the leading correction to the long distance equation in the time-translation invariant case where A(L) = Z |⃗ p|≤1 L /dω/d3pei⃗ p.⃗ x−iωt⟨ Z /dω′/d3k ¯J(⃗k, ω′)¯Φ(⃗ p−⃗k, ω−ω ′)⟩.(78) Now using that space-time invariance is respected, we have ⟨j(⃗k, ω)j(⃗ p, ω′...

  8. [8]

    This can be written as Veff(¯ϕ) = 1 2 m2 ϕ(¯ϕ− ˆϕ)− 1 2 m2 ϕ ˆϕ2 (93) where ˆϕ=− βρ0 mPlm2 ϕ andm 2 ϕ =m 2 0 + β2 m2 Pl B2ρ0 is the mass squared of the cosmological field

    Corrections to the potential The main effect of the short distance fluctuations on the large scale dynamics are encapsulated in the correction to the scalar potential (75) δV= β mPl A(L)B1(¯ϕ).(90) 21 When the model has a quadratic coupling to matter, the coefficientB 1(¯ϕ) is linear B1(¯ϕ) = 1 + β mPl B2 ¯ϕ.(91) A particularly interesting situation corre...

  9. [9]

    this large coupling between scalar and matter is the raison d’ˆ etre of screening and should be screened to avoid large effects of modified gravity

    Screened short scales In the screened case, the large scale fields are perturbations of the short distance ¯Φ and we expand the effective action using B(ϕ+ Φ) = X n≥1 Bn(Φ) n! ( β mPl )nϕn (99) and the interaction potential V(ϕ+ Φ) = X n≥0 Vn(Φ) n! ( β mPl )nϕn.(100) We assume that the expansion is valid as long asβ ϕ mPl ≪1 whereβcan be large, i.e. this ...

  10. [10]

    Unscreened The perturbed Klein-Gordon equation (76) reads □δϕ=W < ⋆((m 2 0 + ( β mPl )3A(L)B3(¯ϕ))δϕ+ β mPl B1(¯ϕ)δj< +ξ) (106) whereϕ= ¯ϕ+δϕandδj < =j < − ¯J0. The mass term is m2 0 =∂ 2 ϕ(V(ϕ) + ¯J0B(ϕ))|ϕ=¯ϕ.(107) 24 The full cosmological mass is corrected by the interaction with the short distance matter distribu- tion M 2 =m 2 0 + ( β mPl )3A(L)B3(¯ϕ...

  11. [11]

    This is the screening criterion guaranteeing that all substructures are screened

    Screened In the screened case and from (102) we have directly in Fourier space δϕ= β mPl ⟨B1(¯Φ)⟩δj<(⃗k, ω) +ξ( ⃗k, ω) ω2 − ⃗k2 −M 2 1k≤ 1 L .(110) We now find that ifM≫Hthe quasi-static perturbations are strongly Yukawa suppressed by the large mass as δϕ(⃗ x, t)∼ −1 4π Z |⃗ x−⃗ y|≤L d3y e−M|⃗ x−⃗ y| |⃗ x−⃗ y|( β mPl B1(¯Φ)δj<(⃗ y, t) +ξ(⃗ y, t)) (111) as...

  12. [12]

    At this order we can then use the equivalence between Gaussian noises ξ(x)≡ β mPl B1(¯ϕ(t))j>(x) (121) relating the noise to the short distance random source

    Unscreened dynamics In this case we have to leading order Γ− ⟨Γ⟩ ≃ β mPl Z d4x√−gj>B1(ϕ+)ϕ−.(115) This implies that the two-point function of the noise term is C2(Γ) 2 ≃ β2 2m2 Pl Z d4xd4y√−gx √−gyB1(ϕ+(x))B1(ϕ+(y))⟨j>(x)j>(y)⟩ϕ−(x)ϕ−(y) (116) leading to the two point function ⟨ξ(x)ξ(y)⟩ ≃ β2 m2 Pl B1(ϕ+(x))B1(ϕ+(y))⟨j>(x)j>(y)⟩.(117) As we have expanded ...

  13. [13]

    In (110) the noise contribution is potentially larger than the source coming from the large scale fluctuationsδj < contrary to the unscreened case

    Screened dynamics In this case the leading order term is Γ− ⟨Γ⟩ ≃ β mPl Z d4x√−g∆ (V1(Φ) + ¯J B1(Φ) ϕ−.(123) Using the minimum equation we have Γ− ⟨Γ⟩ ≃ β mPl Z d4x√−gJ0∆(B1(Φ))ϕ− (124) implying that ⟨ξ(x)ξ(y)⟩ ≃( β mPl )2 ¯J0(t) ¯J0(t′)⟨∆B1(¯Φ)(x)∆B1(¯Φ)(y)⟩(125) As an order of magnitude we haveξ=O(β ¯J0/mPl). In (110) the noise contribution is potential...

  14. [14]

    E. J. Copeland, M. Sami, and S. Tsujikawa, Int. J. Mod. Phys. D15, 1753 (2006), hep-th/0603057

    Pith/arXiv arXiv 2006

  15. [15]

    Joyce, B

    A. Joyce, B. Jain, J. Khoury, and M. Trodden, Phys. Rept.568, 1 (2015), 1407.0059

    Pith/arXiv arXiv 2015

  16. [16]

    Brax, Rept

    P. Brax, Rept. Prog. Phys.81, 016902 (2018)

    2018

  17. [17]

    A. G. Adame et al. (DESI) (2024), 2404.03002

    Pith/arXiv arXiv 2024

  18. [18]

    Lodha et al

    K. Lodha et al. (DESI) (2025), 2503.14743

    Pith/arXiv arXiv 2025

  19. [19]

    Abdul Karim et al

    M. Abdul Karim et al. (DESI) (2025), 2503.14738

    Pith/arXiv arXiv 2025

  20. [20]

    T. M. C. Abbott et al. (DES) (2026), 2605.27221

    Pith/arXiv arXiv 2026

  21. [21]

    Amendola, Phys

    L. Amendola, Phys. Rev. D62, 043511 (2000), astro-ph/9908023

    Pith/arXiv arXiv 2000

  22. [22]

    Brax, Phys

    P. Brax, Phys. Rev. D112, 083544 (2025), 2507.16723

    arXiv 2025

  23. [23]

    Bertotti, L

    B. Bertotti, L. Iess, and P. Tortora, Nature425, 374 (2003)

    2003

  24. [24]

    Archidiacono, E

    M. Archidiacono, E. Castorina, D. Redigolo, and E. Salvioni, JCAP10, 074 (2022), 2204.08484

    arXiv 2022

  25. [25]

    G´ omez-Valent, V

    A. G´ omez-Valent, V. Pettorino, and L. Amendola, Phys. Rev. D101, 123513 (2020), 2004.00610

    arXiv 2020

  26. [26]

    S. Das, P. S. Corasaniti, and J. Khoury, Phys. Rev. D73, 083509 (2006), astro-ph/0510628

    Pith/arXiv arXiv 2006

  27. [27]

    W. J. Wolf, P. G. Ferreira, and C. Garc´ ıa-Garc´ ıa, Phys. Rev. D111, L041303 (2025), 2409.17019

    arXiv 2025

  28. [28]

    Khoury, M.-X

    J. Khoury, M.-X. Lin, and M. Trodden, Phys. Rev. Lett.135, 181001 (2025), 2503.16415

    arXiv 2025

  29. [29]

    Martin, C

    J. Martin, C. Schimd, and J.-P. Uzan, Phys. Rev. Lett.96, 061303 (2006), astro-ph/0510208

    Pith/arXiv arXiv 2006

  30. [30]

    P. Brax, S. Casas, H. Desmond, and B. Elder, Universe8, 11 (2021), 2201.10817

    arXiv 2021

  31. [31]

    Burrage and J

    C. Burrage and J. Sakstein, Living Rev. Rel.21, 1 (2018), 1709.09071

    Pith/arXiv arXiv 2018

  32. [32]

    Khoury and A

    J. Khoury and A. Weltman, Phys. Rev. Lett.93, 171104 (2004), astro-ph/0309300

    Pith/arXiv arXiv 2004

  33. [33]

    Khoury and A

    J. Khoury and A. Weltman, Phys. Rev. D69, 044026 (2004), astro-ph/0309411

    Pith/arXiv arXiv 2004

  34. [34]

    Hinterbichler and J

    K. Hinterbichler and J. Khoury, Phys. Rev. Lett.104, 231301 (2010), 1001.4525

    Pith/arXiv arXiv 2010

  35. [35]

    P. Brax, C. van de Bruck, A.-C. Davis, and D. Shaw, Phys. Rev. D82, 063519 (2010), 1005.3735

    Pith/arXiv arXiv 2010

  36. [36]

    D. F. Mota and D. J. Shaw, Phys. Rev. Lett.97, 151102 (2006), hep-ph/0606204

    Pith/arXiv arXiv 2006

  37. [37]

    C. P. Burgess,Introduction to Effective Field Theory(Cambridge University Press, 2020), ISBN 978- 1-139-04804-0, 978-0-521-19547-8

    2020

  38. [38]

    Huterer, Astron

    D. Huterer, Astron. Astrophys. Rev.31, 2 (2023), 2212.05003

    arXiv 2023

  39. [39]

    J. S. Schwinger, J. Math. Phys.2, 407 (1961)

    1961

  40. [40]

    L. V. Keldysh, Zh. Eksp. Teor. Fiz.47, 1515 (1964)

    1964

  41. [41]

    Colas, Z

    T. Colas, Z. Qin, and X. Tong (2025), 2512.07941

    arXiv 2025

  42. [42]

    C. R. Contaldi and M. Pieroni (2026), 2603.23473

    arXiv 2026

  43. [43]

    S. Shao, B. Li, M. Cautun, H. Wang, and J. Wang, Mon. Not. Roy. Astron. Soc.489, 4912 (2019), 32 1907.02081

    arXiv 2019

  44. [44]

    L. D. Landau and E. M. Lifschitz,Statistical Physics(Pergamon press, 1969)

    1969

  45. [45]

    Asgari, A

    M. Asgari, A. J. Mead, and C. Heymans (2023), 2303.08752

    arXiv 2023

  46. [46]

    Ansari, A

    A. Ansari, A. Banerjee, S. Jain, and S. Padhyegurjar, JCAP10, 018 (2025), 2406.17025

    arXiv 2025

  47. [47]

    Donath, M

    Y. Donath, M. Lewandowski, and L. Senatore, Phys. Rev. D109, 123510 (2024), 2307.11409

    arXiv 2024

  48. [48]

    R. A. Porto, M. M. Riva, and Z. Yang (2024), 2409.05860

    arXiv 2024

  49. [49]

    Brax and E

    P. Brax and E. Bruy` ere, Phys. Rev. D111, 064076 (2025), 2412.15092

    arXiv 2025

  50. [50]

    Kaplanek, M

    G. Kaplanek, M. Mylova, and A. J. Tolley (2025), 2512.17089

    Pith/arXiv arXiv 2025

  51. [51]

    Kaplanek, M

    G. Kaplanek, M. Mylova, and A. J. Tolley (2026), 2604.26941

    Pith/arXiv arXiv 2026

  52. [52]

    C´ espedes and T

    S. C´ espedes and T. Colas (2026), 2605.11096

    Pith/arXiv arXiv 2026

  53. [53]

    Amoruso, G

    R. Amoruso, G. Braga, A. Garoffolo, F. Lopez, N. Bartolo, and S. Matarrese (2026), 2604.15313

    Pith/arXiv arXiv 2026

  54. [54]

    Donath and E

    Y. Donath and E. Pajer, JHEP07, 064 (2024), 2402.05999

    arXiv 2024

  55. [55]

    Smith, P

    A. Smith, P. Brax, C. van de Bruck, C. P. Burgess, and A.-C. Davis, Eur. Phys. J. C85, 1062 (2025), 2505.05450

    arXiv 2025

  56. [56]

    P. Brax, C. van de Bruck, A.-C. Davis, J. Khoury, and A. Weltman, Phys. Rev. D70, 123518 (2004), astro-ph/0408415

    Pith/arXiv arXiv 2004

  57. [57]

    Kittel,Introduction to Solid State Physics(Wiley, 2004)

    C. Kittel,Introduction to Solid State Physics(Wiley, 2004)

    2004