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

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.

• The paper advances Informational Structural Realism by arguing that cross-model informational invariants, rather than internal ontology, capture cosmological truth.
• It employs information geometry and statistical tools like the Fisher–Rao metric to critique the inference of ontological claims from empirical adequacy.
• The study reinterprets cosmological tensions, such as dark matter invariants and the Hubble tension, as manifestations of pipeline- and representation-dependence.

Informational Invariance and the Epistemic Status of Cosmological Models

Introduction

"Cosmology as Representation: Informational Invariance and the Limits of Scientific Realism" (2606.21586) provides a rigorous and philosophically sophisticated critique of the standard scientific realist interpretation of cosmological success. The paper interrogates the ontological inferences often drawn from the empirical and predictive performance of $\Lambda$CDM and related frameworks. It advances an alternative stance, “Informational Structural Realism” (ISR), under which the objective content of cosmological models is identified not with theory-internal ontology but with cross-representational informational invariants: features of statistical structure, observational distinguishability, and accessible information that persist across empirically adequate models. The work synthesizes perspectives from structural realism, information theory, and the epistemology of cosmological inference, grounding its claims in methodological, historical, and technical considerations from both philosophy of science and cosmology.

Methodological Critique and Historical Motivation

The central methodological claim is that empirical adequacy—even of the kind exemplified by $\Lambda$CDM—under-determines both ontology and the formal framework of cosmological description. The argument draws explicit parallels with familiar underdetermination episodes from the history of physics: the fate of the luminiferous ether, caloric theory, and the revisions to Newtonian ontology in the transition to general relativity. These cases underscore that predictive power and theoretical unification, while evidentially significant, do not license direct metaphysical inference to a theory’s object-language ontology.

Cosmology exemplifies several amplifying features:

• Non-replicability and observational embedding: The universe is a unique system, and cosmologists lack the experimental control available in other physical sciences. The inferential base is irreducibly shaped by instrument modeling, foreground cleaning, and statistical post-processing.
• Framework dependence and dualities: Modern physics frequently reveals empirical equivalence among formally and ontologically distinct theories (e.g., dualities in high-energy theory, alternative formulations of quantum mechanics), calling into question claims of representational uniqueness.

This context motivates ontological modesty: the claim that scientific progress in cosmology should not be equated with convergence to a singular, privileged mathematical or ontological description.

Informational Invariance: Theoretical Structure

ISR claims that the most epistemically robust content in cosmology resides at the level of informational invariants—features stable under admissible transformations of representation. The paper isolates three families of such invariants:

1. Correlation Structure: Exemplified by power spectra and higher-order $n$-point correlation functions in the CMB and large-scale structure, these summarize empirical constraints that any successful model must match, irrespective of the underlying ontological encoding.
2. Distinguishability Structure: Formally characterized by the Fisher information metric and its eigenstructure, these capture which linear combinations of parameters or model features are tightly constrained by the data and which are degenerate.
3. Information Bounds: These include cosmic variance limitations, causal horizons, and entropy bounds. They reflect structural constraints on what can, in principle, be inferred by embedded observers.

These invariants are domain-relative but observer-independent in a physically meaningful sense: they are stable for any agent with equivalent observational access.

Information Geometry as Operational Backbone

A central technical contribution is the elaboration of information geometry as the precise framework for ISR’s invariance criterion. The Fisher–Rao metric, unique as a Riemannian metric invariant under sufficient statistics, encodes statistical distinguishability in model space independent of parameterization. Degeneracy directions (zero or small eigenvalues) correspond to physically meaningful indistinguishabilities, not pathologies of inferential practice.

The Kullback–Leibler divergence is used to extend the equivalence-class perspective to finite distances in model space: two models belong to the same class if their predicted data distributions are empirically indistinguishable at an achievable threshold. This formalism captures both local (Fisher) and global (KL) aspects of cross-model invariance, unifying data-driven epistemic constraints with theory-independent metrics.

The framework also aligns ISR with Bayesian cosmological practice, distinguishing between inference results robust under variations of parameterization and prior (invariant under representation) versus those that are not.

Comparison to Competing Positions

The philosophical position of ISR is articulated in relation to:

• Ontic Structural Realism (OSR): Unlike OSR, ISR does not locate objectivity within the formal structure of any one theory but in the invariants that survive across empirically adequate representations. ISR addresses the persistent problem in structural realism regarding the distinction between physical structure and formal artifact.
• Constructive Empiricism: ISR diverges by ascribing objective significance to informational invariants not limited to direct observables but including statistical and inferential structure about what constraints the world imposes on possible representations.
• Traditional Realism: ISR refutes the direct inference from empirical success to ontological truth, instead rooting realism at the level of the empirical and inferential constraints any successful description must respect.

Case Studies: Dark Matter, Hubble Tension, and Cosmological Tensions

The ISR framework is applied to contemporary cosmological issues:

• Dark Matter: The robust achievement is not the identification of the microphysical ontology of dark matter, but the establishment of an invariant pattern in cross-probe correlation structures (e.g., rotation curves, lensing, CMB peak positions).
• Hubble Tension and Other Tensions: Discrepancies between inference pipelines (e.g., CMB-inferred $H_0$ vs. local SH0ES measurements) are interpreted not as direct measurements of the same parameter, but as structural inconsistencies between informational constraints imposed by different domains and analysis procedures. This approach emphasizes the pipeline- and representation-dependence of specific claims, and the domain-invariance of the contradiction itself.

Implications and Limits

ISR does not conflate invariance with fundamentality; the paper is explicit that the identification of information geometry invariants as ontologically robust is a philosophical, not purely formal, move. The criterion for admissible representations is operational yet non-trivial, excluding pathologies while admitting the plurality endemic to cosmology.

Practically, ISR reframes scientific progress in cosmology as the refinement of informational structure—splitting of equivalence classes and resolution of degeneracies—rather than as convergence to a unique, fixed ontology. This shift is especially pertinent for the interpretation of ambiguous or evolving data, such as varying constraints on the dark energy equation of state, which depend sensitively on the inference pipeline.

Conclusion

"Cosmology as Representation: Informational Invariance and the Limits of Scientific Realism" (2606.21586) advances a rigorous framework—ISR—for epistemic commitment in cosmological science, rooted in information theory and formal epistemology. It challenges the direct inference from empirical adequacy to ontological commitment, instead advocating realism about invariants of informational structure manifest across frameworks and representations. The theoretical and methodological consequences are significant: ISR recasts cosmological inquiry as the progressive clarification of the inferential and statistical constraints the universe imposes on observational structure, fundamentally distinct from the discovery of a singular underlying ontology. The framework is positioned to integrate naturally with future theoretical and observational developments, providing a principled stance for interpreting cosmological progress in an age of growing representational plurality and empirical tension.