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arxiv: 2606.21586 · v1 · pith:XYXMF5P6new · submitted 2026-06-19 · ⚛️ physics.hist-ph · astro-ph.CO· hep-ph· hep-th

Cosmology as Representation: Informational Invariance and the Limits of Scientific Realism

Stefano Profumo This is my paper

Pith reviewed 2026-06-26 12:51 UTC · model grok-4.3

classification ⚛️ physics.hist-ph astro-ph.COhep-phhep-th
keywords cosmologyscientific realisminformational invariantsunderdeterminationobservational structureFisher-Rao metricphilosophy of science
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The pith

Cosmology's objective content consists of informational invariants preserved across models rather than any particular ontology.

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

The paper argues that cosmology does not provide an increasingly accurate picture of the universe's underlying reality even as its models improve. What remains stable and objective across different empirically successful models are certain features of the observational data itself, described in information terms such as correlations and limits on distinguishability. These features can be tracked with tools like the Fisher-Rao metric on the space of models. A sympathetic reader would care because this reframes progress in cosmology as refinement of accessible data patterns instead of convergence on fundamental truths about what exists.

Core claim

The objective content of cosmology is best identified with cross-representational informational invariants—features of observational structure that persist across empirically adequate descriptions. These invariants can be characterized in information-theoretic terms, including correlation structure, statistical distinguishability, and limits on accessible information, and formalized using tools such as the Fisher-Rao metric on model space. Cosmological models are best understood as efficient encodings of observational structure rather than uniquely privileged descriptions of fundamental reality. Scientific progress consists not in convergence toward a fixed ontology, but in the progressive r

What carries the argument

Cross-representational informational invariants: features of observational structure that persist across empirically adequate descriptions, tracked via information-theoretic measures including the Fisher-Rao metric.

If this is right

  • Scientific progress in cosmology consists in refining the informational structure accessible to observation rather than approaching a fixed ontology.
  • Models function as efficient encodings of observational structure rather than direct pictures of fundamental reality.
  • Empirical adequacy leaves multiple frameworks viable for representing the same data.
  • Limits on accessible information and statistical distinguishability remain stable even when models change.

Where Pith is reading between the lines

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

  • The same emphasis on invariants might apply to other underdetermined domains such as quantum gravity where multiple frameworks fit current data.
  • Future surveys could check whether newly measured correlations remain invariant when re-expressed in alternative model languages.
  • If invariants prove robust, cosmology would resemble a form of data compression whose success is measured by retained structure rather than ontological accuracy.

Load-bearing premise

The empirical success of cosmology underdetermines not only ontology but also the mathematical and conceptual frameworks used to represent observational data.

What would settle it

A demonstration that cosmological observations uniquely fix one mathematical framework or ontology across all empirically adequate models would refute the claim that underdetermination extends to frameworks.

read the original abstract

Modern cosmology is often taken to provide an increasingly accurate description of the universe's underlying ontology through progressively refined mathematical models. I challenge this interpretation by arguing that the empirical success of cosmology underdetermines not only ontology but also the mathematical and conceptual frameworks used to represent observational data. I propose instead that the objective content of cosmology is best identified with cross-representational informational invariants-features of observational structure that persist across empirically adequate descriptions. These invariants can be characterized in information-theoretic terms, including correlation structure, statistical distinguishability, and limits on accessible information, and formalized using tools such as the Fisher-Rao metric on model space. On this view, cosmological models are best understood as efficient encodings of observational structure rather than uniquely privileged descriptions of fundamental reality. Scientific progress, accordingly, consists not in convergence toward a fixed ontology, but in the progressive refinement of the informational structure accessible to observation.

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 / 1 minor

Summary. The paper challenges the realist interpretation of modern cosmology, arguing that empirical success underdetermines not only ontology but also the mathematical and conceptual frameworks for representing data. It proposes that objective content resides in cross-representational informational invariants (e.g., correlation structure, statistical distinguishability, limits on accessible information), which can be formalized using tools such as the Fisher-Rao metric on model space. Cosmological models are thus viewed as efficient encodings of observational structure rather than privileged descriptions of reality, with scientific progress consisting in refinement of accessible informational structure.

Significance. If the central proposal holds, the manuscript offers a coherent philosophical alternative to standard realism debates in cosmology by grounding objectivity in invariants rather than ontology. It explicitly engages information-theoretic tools and underdetermination arguments, providing a framework that could clarify the limits of model equivalence in observational cosmology. No machine-checked proofs or reproducible code are present, but the argument is internally consistent from its premises.

major comments (2)
  1. [Abstract] Abstract and introduction: The claim that invariants 'can be characterized in information-theoretic terms... and formalized using tools such as the Fisher-Rao metric on model space' is load-bearing for the proposal that objective content is independently identifiable, yet no derivation, explicit definition of the metric in this context, or worked cosmological example is supplied to show how such invariants are extracted or distinguished from mere model equivalence.
  2. [Introduction] The weakest assumption (empirical success underdetermines representational frameworks) is stated but not tested against specific cases; without at least one concrete pair of empirically adequate but representationally distinct cosmological models (e.g., FLRW vs. alternative metric representations of the same data), the move from underdetermination to informational invariants remains a restatement rather than an independent grounding.
minor comments (1)
  1. Notation for 'informational invariants' is introduced without a compact symbol or formal definition, which would aid clarity when contrasting with standard realist ontology.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and the identification of points where the central proposal would benefit from greater explicitness. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract and introduction: The claim that invariants 'can be characterized in information-theoretic terms... and formalized using tools such as the Fisher-Rao metric on model space' is load-bearing for the proposal that objective content is independently identifiable, yet no derivation, explicit definition of the metric in this context, or worked cosmological example is supplied to show how such invariants are extracted or distinguished from mere model equivalence.

    Authors: The manuscript advances a philosophical framework in which the Fisher-Rao metric is cited as one established tool from information geometry that can be used to formalize cross-representational invariants; the paper does not claim to supply a new derivation. We agree that an illustrative sketch would make the load-bearing claim more transparent. In revision we will insert a concise paragraph (new subsection or expanded introduction) that (i) recalls the definition of the Fisher-Rao metric on a statistical manifold and (ii) applies it to a minimal cosmological example (parameter estimation from distance-redshift data) to show how an invariant correlation structure is distinguished from representational choice. revision: yes

  2. Referee: [Introduction] The weakest assumption (empirical success underdetermines representational frameworks) is stated but not tested against specific cases; without at least one concrete pair of empirically adequate but representationally distinct cosmological models (e.g., FLRW vs. alternative metric representations of the same data), the move from underdetermination to informational invariants remains a restatement rather than an independent grounding.

    Authors: The underdetermination premise is drawn from the existing literature on cosmological degeneracies. We accept that a single, explicitly worked pair would render the subsequent move to informational invariants more robust. In the revised introduction we will add a short paragraph presenting one such pair—e.g., the observational equivalence between a flat FLRW model with a dynamical dark-energy equation of state and a certain class of modified-gravity metrics that reproduce identical luminosity-distance and CMB power-spectrum data—while differing in their representational primitives, thereby isolating the shared informational invariants. revision: yes

Circularity Check

0 steps flagged

No significant circularity in philosophical argument

full rationale

The paper advances a philosophical reinterpretation rather than a formal derivation chain. Its central claim—that objective cosmological content consists in cross-representational informational invariants—follows from the stated premise of underdetermination of both ontology and representational frameworks. No equations, fitted parameters, self-citations, or ansatzes are invoked that reduce the conclusion to the inputs by construction. The Fisher-Rao metric is mentioned only as a possible formalization tool, not as part of a load-bearing derivation. The argument is self-contained as an interpretive stance and does not match any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on the abstract alone, the paper rests on the standard domain assumption in philosophy of science that empirical adequacy underdetermines ontology and frameworks; no free parameters, invented entities, or ad-hoc axioms are introduced.

axioms (1)
  • domain assumption Empirical success of cosmological models underdetermines both ontology and the mathematical frameworks used to represent data
    Invoked in the opening sentences as the premise being challenged to motivate the informational-invariants alternative.

pith-pipeline@v0.9.1-grok · 5679 in / 1338 out tokens · 35998 ms · 2026-06-26T12:51:52.018819+00:00 · methodology

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Reference graph

Works this paper leans on

211 extracted references · 2 canonical work pages · 2 internal anchors

  1. [1]

    2008 , publisher =

    Weinberg, Steven , title =. 2008 , publisher =

    2008

  2. [2]

    and Reid, Beth A

    Percival, Will J. and Reid, Beth A. and Eisenstein, Daniel J. and others , title =. Monthly Notices of the Royal Astronomical Society , volume =. 2010 , doi =

    2010

  3. [3]

    and Macri, Lucas M

    Riess, Adam G. and Macri, Lucas M. and Hoffmann, Samantha L. and others , title =. The Astrophysical Journal , volume =. 2016 , doi =

    2016

  4. [4]

    2017 , publisher =

    Callender, Craig , title =. 2017 , publisher =

    2017

  5. [5]

    1999 , publisher =

    Psillos, Stathis , title =. 1999 , publisher =

    1999

  6. [6]

    , title =

    Wigner, Eugene P. , title =. Communications on Pure and Applied Mathematics , year =

  7. [7]

    Radhakrishna , title =

    Rao, C. Radhakrishna , title =. Bulletin of the Calcutta Mathematical Society , volume =

  8. [8]

    The Oxford Handbook of Philosophy of Physics , editor =

    Smeenk, Chris , title =. The Oxford Handbook of Philosophy of Physics , editor =

  9. [9]

    Studies in History and Philosophy of Science Part B , volume =

    Smeenk, Chris , title =. Studies in History and Philosophy of Science Part B , volume =

  10. [10]

    1982 , note =

    Statistical Decision Rules and Optimal Inference , publisher =. 1982 , note =

    1982

  11. [11]

    afer, Bj\

    Giesel, Eileen and Reischke, Robert and Sch\"afer, Bj\"orn Malte and Chia, Dominic , title =. Journal of Cosmology and Astroparticle Physics , volume =. 2021 , doi =. 2005.01057 , archivePrefix =

    arXiv 2021

  12. [12]

    Galilei, Galileo , title =

  13. [13]

    Discoveries and Opinions of Galileo , editor =

    Galilei, Galileo , title =. Discoveries and Opinions of Galileo , editor =. 1957 , pages =

    1957

  14. [14]

    Dialectica , volume =

    Worrall, John , title =. Dialectica , volume =. 1989 , doi =

    1989

  15. [15]

    2020 , doi =

    Astronomy & Astrophysics , volume =. 2020 , doi =. 1807.06209 , archivePrefix =

    Pith/arXiv arXiv 2020

  16. [16]

    Martens, Niels C. M. , title =. Foundations of Physics , volume =. 2022 , doi =

    2022

  17. [17]

    Studies in the History and Philosophy of Modern Physics , keywords =

    Evidence of dark matter, and the interpretive role of general relativity. Studies in the History and Philosophy of Modern Physics , keywords =

  18. [18]

    Mathematics, Matter and Method: Philosophical Papers, Volume 1 , publisher =

    Putnam, Hilary , title =. Mathematics, Matter and Method: Philosophical Papers, Volume 1 , publisher =. 1975 , pages =

    1975

  19. [19]

    Relativism and Realism in Science , year =

    Musgrave, Alan , title =. Relativism and Realism in Science , year =

  20. [20]

    1954 , note =

    Duhem, Pierre , title =. 1954 , note =

    1954

  21. [21]

    Erkenntnis , volume =

    Quine, Willard Van Orman , title =. Erkenntnis , volume =. 1975 , doi =

    1975

  22. [22]

    , title =

    van Fraassen, Bas C. , title =

  23. [23]

    Philosophy of Science , volume =

    Laudan, Larry , title =. Philosophy of Science , volume =. 1981 , doi =

    1981

  24. [24]

    , title =

    Kuhn, Thomas S. , title =

  25. [25]

    Kyle , title =

    Stanford, P. Kyle , title =

  26. [26]

    Ladyman, James and Ross, Don and Spurrett, David and Collier, John , title =

  27. [27]

    Philosophy of Science , volume =

    Weatherall, James Owen , title =. Philosophy of Science , volume =. 2019 , doi =

    2019

  28. [28]

    Philosophy Compass , volume =

    Weatherall, James Owen , title =. Philosophy Compass , volume =. 2019 , doi =

    2019

  29. [29]

    Synthese , volume =

    Floridi, Luciano , title =. Synthese , volume =. 2008 , doi =

    2008

  30. [30]

    , title =

    Dennett, Daniel C. , title =. The Journal of Philosophy , volume =. 1991 , doi =

    1991

  31. [31]

    Studies in History and Philosophy of Science Part A , volume =

    Ladyman, James , title =. Studies in History and Philosophy of Science Part A , volume =. 1998 , doi =

    1998

  32. [32]

    French, Steven , title =

  33. [33]

    Newton, Isaac , title =

  34. [34]

    Laplace, Pierre-Simon , title =

  35. [35]

    Earman, John , title =

  36. [36]

    , title =

    Wald, Robert M. , title =

  37. [37]

    Mathematical Proceedings of the Cambridge Philosophical Society , volume =

    Schr\"odinger, Erwin , title =. Mathematical Proceedings of the Cambridge Philosophical Society , volume =. 1935 , doi =

    1935

  38. [38]

    , title =

    Bell, John S. , title =. Physics , volume =

  39. [39]

    Physical Review Letters , volume =

    Aspect, Alain and Dalibard, Jean and Roger, G\'erard , title =. Physical Review Letters , volume =. 1982 , doi =

    1982

  40. [40]

    and Bernien, H

    Hensen, B. and Bernien, H. and Dr\'eau, A. E. and others , title =. Nature , volume =. 2015 , doi =

    2015

  41. [41]

    Studies in History and Philosophy of Science Part A , volume =

    Howard, Don , title =. Studies in History and Philosophy of Science Part A , volume =. 1985 , doi =

    1985

  42. [42]

    The British Journal for the Philosophy of Science , volume =

    Teller, Paul , title =. The British Journal for the Philosophy of Science , volume =

  43. [43]

    , title =

    Bell, John S. , title =

  44. [44]

    Topoi , volume =

    Maudlin, Tim , title =. Topoi , volume =. 1995 , doi =

    1995

  45. [45]

    Reviews of Modern Physics , volume =

    Everett, Hugh , title =. Reviews of Modern Physics , volume =. 1957 , doi =

    1957

  46. [46]

    Physical Review , volume =

    Bohm, David , title =. Physical Review , volume =. 1952 , doi =

    1952

  47. [47]

    Physical Review D , volume =

    Ghirardi, Gian Carlo and Rimini, Alberto and Weber, Tullio , title =. Physical Review D , volume =. 1986 , doi =

    1986

  48. [48]

    , title =

    Albert, David Z. , title =

  49. [49]

    Physical Review , volume =

    Bohr, Niels , title =. Physical Review , volume =. 1935 , doi =

    1935

  50. [50]

    Heisenberg, Werner , title =

  51. [51]

    1932 , note =

    von Neumann, John , title =. 1932 , note =

    1932

  52. [52]

    , title =

    DeWitt, Bryce S. , title =. Physical Review , volume =. 1967 , doi =

    1967

  53. [53]

    Battelle Rencontres: 1967 Lectures in Mathematics and Physics , editor =

    Wheeler, John Archibald , title =. Battelle Rencontres: 1967 Lectures in Mathematics and Physics , editor =. 1968 , pages =

    1967

  54. [54]

    and Hawking, Stephen W

    Hartle, James B. and Hawking, Stephen W. , title =. Physical Review D , volume =. 1983 , doi =

    1983

  55. [55]

    , title =

    Hawking, Stephen W. , title =. Nuclear Physics B , volume =. 1984 , doi =

    1984

  56. [56]

    , title =

    Isham, Christopher J. , title =. NATO Science Series C , volume =. 1993 , doi =

    1993

  57. [57]

    , title =

    Griffiths, Robert B. , title =. Journal of Statistical Physics , volume =. 1984 , doi =

    1984

  58. [58]

    Reviews of Modern Physics , volume =

    Omn\`es, Roland , title =. Reviews of Modern Physics , volume =. 1992 , doi =

    1992

  59. [59]

    , title =

    Gell-Mann, Murray and Hartle, James B. , title =. Physical Review D , volume =. 1993 , doi =

    1993

  60. [60]

    Wallace, David , title =

  61. [61]

    International Journal of Theoretical Physics , volume =

    Rovelli, Carlo , title =. International Journal of Theoretical Physics , volume =. 1996 , doi =

    1996

  62. [62]

    Kiefer, Claus , title =

  63. [63]

    Philosophy of Science , volume =

    W\"uthrich, Christian , title =. Philosophy of Science , volume =. 2005 , doi =

    2005

  64. [64]

    and Mermin, N

    Fuchs, Christopher A. and Mermin, N. David and Schack, R\"udiger , title =. American Journal of Physics , volume =. 2014 , doi =

    2014

  65. [65]

    On the Quantum Measurement Problem , journal =

    Brukner,. On the Quantum Measurement Problem , journal =. 2017 , publisher =

    2017

  66. [66]

    Healey, Richard , title =

  67. [67]

    Polchinski, Joseph , title =

  68. [68]

    International Journal of Modern Physics A , volume =

    Sen, Ashoke , title =. International Journal of Modern Physics A , volume =. 1994 , doi =

    1994

  69. [69]

    and Townsend, Paul K

    Hull, Christopher M. and Townsend, Paul K. , title =. Nuclear Physics B , volume =. 1995 , doi =

    1995

  70. [70]

    International Journal of Theoretical Physics , volume =

    Maldacena, Juan , title =. International Journal of Theoretical Physics , volume =. 1999 , doi =

    1999

  71. [71]

    Advances in Theoretical and Mathematical Physics , volume =

    Witten, Edward , title =. Advances in Theoretical and Mathematical Physics , volume =. 1998 , doi =

    1998

  72. [72]

    Studies in History and Philosophy of Modern Physics , volume =

    Rickles, Dean , title =. Studies in History and Philosophy of Modern Physics , volume =. 2013 , doi =

    2013

  73. [73]

    Dawid, Richard , title =

  74. [74]

    Motivating Dualities , journal =

    Read, James and M. Motivating Dualities , journal =. 2020 , doi =

    2020

  75. [75]

    Philosophy of Science , volume =

    Menon, Tushar , title =. Philosophy of Science , volume =. 2019 , doi =

    2019

  76. [76]

    Dualities and Emergent Gravity: Gauge/Gravity Duality

    de Haro, Sebastian. Dualities and Emergent Gravity: Gauge/Gravity Duality. Stud. Hist. Phil. Sci. B. 2017. doi:10.1016/j.shpsb.2015.08.004. arXiv:1501.06162

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.shpsb.2015.08.004 2017

  77. [77]

    A Schema for Duality, Illustrated by Bosonization

    de Haro, Sebastian and Butterfield, Jeremy. A Schema for Duality, Illustrated by Bosonization. 2017. arXiv:1707.06681

    Pith/arXiv arXiv 2017

  78. [78]

    Dirac, Paul A. M. , title =

  79. [79]

    , title =

    Feynman, Richard P. , title =. Reviews of Modern Physics , volume =. 1948 , doi =

    1948

  80. [80]

    Muller, F. A. , title =. Studies in History and Philosophy of Modern Physics , volume =. 1997 , doi =

    1997

Showing first 80 references.