Abstract. The Universe possesses none of the functional criteria by which a living organism is identified. No global metabolism, no active boundary, no mechanism of repair and no finality are known for it. The comparison with the living nevertheless retains a heuristic value when it bears on a more general property: the emergence of a collective dynamic out of local transformations, gradients, flows and interactions between several scales.
Modern cosmology describes global evolution from a homogeneous and isotropic background on which structures develop. This approximation remains remarkably effective. Since Einstein's equations are non-linear, however, the passage from an inhomogeneous space-time to an average geometry is not a neutral operation. The problem of cosmological backreaction seeks to quantify the contributions produced by regional variations of expansion, curvature and shear.
This article presents the foundations of relativistic averaging, Buchert's formalism, the timescape model, recent DESI results, the H₀ tension, the role of gravitational sirens and the contribution of relativistic simulations. The thesis defended remains limited: the progressive organisation of matter could take part in the effective cosmic dynamics, without that possibility being demonstrated today or authorising us to call the Universe alive.
| EPISTEMIC STATUS | |
|---|---|
| Established | General relativity couples matter-energy and geometry. ΛCDM successfully describes a very wide set of observations. |
| Open | The cosmological amplitude of backreaction, the nature of dark energy and the origin of the tensions between certain probes remain debated. |
| Hypothesis examined | Non-linear structuring could contribute to the effective dynamics or to the relation between average quantities and observables. |
Cosmic expansion does not correspond to a biological growth of the Universe. It describes the evolution of the geometry that relates large distances. Galaxies, clusters and voids are not carried along in an external medium expanding around them. On large scales, the distances between unbound regions evolve with the metric of space-time.
Matter nevertheless remains involved in this dynamic. It aggregates, collapses, forms stars, galaxies, filaments and clusters. Underdense regions become voids that occupy a growing share of the cosmic volume. This structuring locally modifies curvature, velocities, gravitational potentials and expansion rates.
Standard cosmology represents the Universe by a homogeneous and isotropic background completed by perturbations. This method describes with remarkable precision the cosmic microwave background, primordial nucleosynthesis, baryon acoustic oscillations and much of structure formation. Its effectiveness does not, however, imply that every consequence of inhomogeneity is necessarily contained in the separation between average background and perturbations.
The problem lies at the passage from local to global. Einstein's equations are non-linear. When density contrasts become large, averaging the geometry and then evolving it does not necessarily give the same result as evolving the regions before averaging them. Cosmological backreaction studies this difference and seeks to measure its real importance.
CENTRAL FORMULATION The Universe might share with the living a more general property: an evolving organisation issuing from transformations, gradients and interactions between several scales. The analogy bears on emergence and backreaction, not on biological functions. |
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1. An operative analogy without assimilation to the living
Living systems maintain themselves far from equilibrium thanks to continuous exchanges of matter and energy. Their continuity depends on organised relations, gradients, cycles and regulations that persist despite the renewal of components. Applied to the Universe, this property retains only a heuristic value and draws attention to the causal role of relations between scales.
The work of Ilya Prigogine showed that organised structures can appear in systems traversed by flows and subject to irreversible processes. Harold Morowitz studied the role of energy flows in biological organisation. Lee Smolin explored, in a different register, historical and evolutionary conceptions of cosmology. These programmes describe neither the same objects nor the same mechanisms. Bringing them together remains conceptual.
The common core lies in a sober proposition: a macroscopic dynamic can depend on non-linear local relations, on their history and on their organisation across several levels of scale. The living provides a particularly elaborate example of this, without necessarily holding a monopoly on it.
In this article the term organisation designates the structure of the relations and correlations linking different regions and scales, beyond mean density and two-point correlations alone. This organisation is operationalised by quantities that project some of its effects onto the average dynamics, notably the distribution of expansion rates, shear, the average curvature ⟨R⟩D and the term QD. Higher-order correlations, such as the bispectrum and trispectrum, describe other statistical signatures of it. None of these quantities constitutes by itself a complete measure of the organisation. Their interest lies in the possibility of relating a multi-scale structure to a dynamic contribution or to an observable difference.
The term « organisation » designates neither a new fundamental quantity nor a single cosmological parameter. It gathers a class of multi-scale structures whose effects must be operationalised separately. The general framework has no single test of refutation. It is the precise mechanisms that give it dynamic content — an averaging prescription, a timescape model or a hypothesis about higher-order correlations — that must produce their own predictions and their own conditions of invalidation.
The demarcation remains indispensable. No global metabolism, no functional boundary, no region of viability, no mechanism of repair and no finality are established for the Universe taken as a whole. Biological vocabulary becomes misleading as soon as it attributes to the cosmos functions that are not observed.
The analogy with non-equilibrium systems concerns internal mechanisms of structuring and interactions between scales. It does not allow the entire Universe to be called a dissipative structure in the strict thermodynamic sense, for want of a functional boundary, an external reservoir and a sustained global flow.
The analogy retains its value when it shifts the analysis from isolated components toward couplings, constraints and feedbacks. It becomes scientific only when it issues in defined variables, quantitative predictions and criteria of refutation.
2. Matter, geometry and averaging
Classical mechanics allows space and time to be represented as a framework within which objects evolve. General relativity abandons this separation. The geometry of space-time depends on physical content, while that geometry influences trajectories, clocks and the propagation of signals.
Einstein's equations condense this coupling:
Gμν + Λgμν = (8πG/c4) Tμν
The tensor Gμν describes curvature. The tensor Tμν represents matter, energy, pressure and flows. The term Λgμν introduces the cosmological constant. Matter does not evolve within a geometry external to it. It contributes to determining that geometry, which then orients its evolution.
This reciprocity is already contained in general relativity. Any novelty would concern the importance taken on by non-linear structuring in the passage to an average cosmological description.
From local to global: the averaging problem. On large scales, standard cosmology uses a Friedmann–Lemaître–Robertson–Walker geometry, homogeneous and isotropic. Galaxies, clusters and voids are described as structures developed from initial perturbations on this background.
This separation performs remarkably well. It allows global parameters to be extracted from the cosmic microwave background, supernovae, BAO and the distribution of galaxies. The averaging problem appears when contrasts become strongly non-linear and regions no longer share the same local history of expansion.
The non-linearity of the equations may be summarised by the following expression:
⟨Gμν[g]⟩ ≠ Gμν[⟨g⟩]
The left-hand side represents the average of the equations applied to local geometries. The right-hand side corresponds to the equations applied directly to an average geometry. No general identity guarantees their equivalence.
The difference results from the change of scale within a non-linear theory. Fluctuations of density, curvature, expansion and shear can produce effective terms when averaged.
The difficulty is also observational. Instruments do not directly measure an average geometry. They record photons, spectral shifts, galaxy shapes and gravitational signals that have crossed a structured Universe. An average theory must relate its variables to these observables without silently imposing the geometry it is trying to test.
Buchert's formalism. Thomas Buchert developed a formalism allowing certain scalar quantities to be averaged in inhomogeneous cosmologies. For a spatial domain D, the average of a quantity Ψ and the effective scale factor associated with the volume are written:
⟨Ψ⟩D = (1/VD) ∫D Ψ√g d3x
aD(t) = [VD(t)/VD(t₀)]1/3
In the case of matter treated as irrotational dust, without pressure or vorticity, the averaged equations take a form close to the Friedmann equations:
3(ȧD/aD)2 = 8πG⟨ρ⟩D − ½⟨R⟩D − ½QD + Λ
3äD/aD = −4πG⟨ρ⟩D + QD + Λ
The kinematical backreaction term is defined by:
QD = ⅔(⟨θ2⟩D − ⟨θ⟩D2) − 2⟨σ2⟩D
The quantity θ describes local expansion and σ the shear. The first term measures the variance of expansion rates within the domain. The second expresses the effect of anisotropic deformations. A heterogeneous distribution of expansion rates can thus contribute to an effective dynamic different from that of a homogeneous model possessing only the same mean density.
The formalism shows that a backreaction can exist. It does not demonstrate that it has the amplitude needed to explain cosmic acceleration. Nor does it supply, by itself, a unique average metric or the whole chain relating the averaged variables to the propagation of light.
The choice of foliation is not a mere freedom of notation. It determines the hypersurfaces on which volumes, expansion rates and average quantities are defined. The aim is not to make the backreaction term independent of any foliation, but to specify the class of observers and the physical slicing to which it refers, and then to build covariant predictions on the light cone. The relevance of an effective cosmology depends on the coherence between that geometric prescription and the distances, spectral shifts, lensing and other observables. Recent work on multi-scale structure shows that the debate does not reduce to a simple opposition between zero backreaction and dominant backreaction.
The averaging problem also concerns the past light cone, where sources are seen at different epochs after propagation through an inhomogeneous geometry. Light-cone averaging approaches provide a complementary framework for relating effective quantities to the distances, spectral shifts and lensing actually observed. The formalism of Gasperini, Marozzi and their co-authors introduces for this purpose generalised commutation rules and observational backreaction terms proper to light-cone averaging. These contributions are distinct from the spatial term QD and complete its interpretation by relating inhomogeneities to the distances and spectral shifts actually observed.
The term QD is not a direct observable. Its effects must be inferred through the relations a model establishes between average expansion, effective curvature, distances, structure growth and the propagation of light. A joint constraint on H(z), cosmological distances, fσ₈(z), lensing and matter clustering can reduce the space of values compatible with a given backreaction, without reconstructing QD uniquely. This inference remains dependent on the averaging prescription, the foliation and the adopted link between spatial hypersurfaces and the light cone.
3. An amplitude still debated
The mathematical existence of backreaction terms and their cosmological importance are two distinct problems. A contribution may be non-zero while remaining too weak to modify average expansion appreciably.
Many simulations and perturbative approaches close to ΛCDM obtain modest global corrections. These results support the idea that the homogeneous background remains an excellent approximation for a wide class of observables. Other work stresses the role of scales, of the slicing of space-time, of average curvature and of the way observations are reconstructed.
The problem predates contemporary debates about dark energy. George Ellis formulated it as early as 1984 in the form of the fitting problem, devoted to fitting a smooth model to an irregular Universe without effacing the dynamic effects produced by the change of scale. The problem bears at once on the average geometry, the observers and the relation between the fitted model and the data.
In the mid-2000s, Edward Kolb, Sabino Matarrese and Antonio Riotto explored the possibility that an effective acceleration might result from the backreaction of cosmological perturbations, without dark energy. This proposal stimulated an intense debate on the control of perturbative orders, on gauge dependence and on the necessity of relating any average acceleration to observables. Akihiro Ishibashi and Robert Wald showed in particular that an averaged scale factor can accelerate without necessarily producing the observed cosmological signal, and that an uncontrolled perturbative approximation does not suffice to establish a dominant backreaction.
Syksy Räsänen then showed, in a simplified analytical model founded on the exact averaging equations for dust, that the coexistence of expanding and collapsing regions can accelerate the average volume expansion. This result establishes a dynamic possibility, not an observational demonstration. It makes explicit the difference between the existence of a mechanism and its capacity to reproduce the real Universe quantitatively.
The most restrictive argument was formulated by Stephen Green and Robert Wald. Within their weak-limit framework applied to small-scale inhomogeneities, under precise assumptions including the weak energy condition — which requires that the energy density measured by any timelike observer be non-negative — the effective stress-energy tensor produced by backreaction is traceless and likewise satisfies that condition. It cannot reproduce the behaviour of a cosmological constant.
Thomas Buchert and his co-authors contested the general reach of this conclusion. They argue that the Green–Wald framework does not constitute a non-local averaging of the geometry and does not necessarily capture the multiscale effects sought by relativistic averaging approaches. The disagreement bears less on the internal coherence of the demonstrations than on their assumptions, their domain of application and the class of effects they represent.
The literature does not supply a single conclusion for all regimes. It rather establishes a hierarchy. Environmental and regional effects may be significant. Their translation into a global modification comparable to dark energy remains far harder to demonstrate.
Backreaction cannot be used as an automatic replacement for Λ. It must produce an expansion history, distances, a growth of structures and lensing signatures compatible with the data. A local improvement of a fit does not suffice.
Voids, dense regions and the timescape model. The cosmic web is strongly hierarchical. Galaxies occupy mainly filaments, nodes and clusters, while voids represent a growing share of the volume. Underdense regions expand faster than dense ones. Gravitationally bound structures cease to follow cosmic expansion in the same way as the surrounding medium.
Standard cosmology already incorporates much of these effects into perturbation theory, simulations and peculiar velocities. Inhomogeneous approaches examine an additional possibility: the distribution of volumes, curvatures and expansion rates might take part in defining the average dynamics itself.
The timescape model, developed by David Wiltshire, proposes a particular interpretation of this idea. It distinguishes large voids from denser regions containing galaxies. These environments have different histories of expansion and curvature. The model also introduces a distinction between the time associated with a volume average and the proper time measured by observers situated within bound structures.
Within this framework, part of the apparent acceleration results from the way clocks, distances and expansion rates are compared between regions whose geometric histories differ. Timescape does not amount to placing the observer at the centre of a spherical void. It modifies the relation between the cosmic average, the observers and the measured parameters.
A recent reanalysis of the Pantheon+ catalogue reported a strong Bayesian preference for timescape within the statistical framework used. The result is notable because it bears on the complete sample and seeks to reduce certain dependences on the cosmology assumed during standardisation. It does not replace a global confrontation with BAO, the cosmic microwave background, structure growth, lensing and cluster observations.
A fair test of a non-FLRW model may require redoing part of the chain by which observables are extracted. Directly reusing parameters calibrated under a standard geometry risks introducing a dependence on the competing model. This point is at once a methodological difficulty and a requirement of rigour.
This methodological requirement does not reduce the burden of proof. A non-FLRW model must recover, within their domains of validity, the principal successes of ΛCDM for the cosmic microwave background, BAO, nucleosynthesis, structure growth and lensing, while showing that its reinterpretation of the observables brings a measurable and coherent gain.
The confrontation with the cosmic microwave background and BAO does not start from nothing. Nazer and Wiltshire fitted the multipoles 50 ≤ ℓ ≤ 2500 to the Planck data, covering the principal acoustic peaks of the temperature spectrum. The best likelihoods obtained were comparable to those of ΛCDM over that range. The analysis nevertheless rested on matching the timescape expansion history to codes designed for an FLRW cosmology close to the standard model at early times. The different matching prescriptions introduced systematic uncertainties of about 8% on the dressed Hubble constant and 13% on the present void volume fraction. These results constitute a substantial test of the model, without yet being equivalent to a complete modern chain incorporating the full temperature, polarisation and lensing spectra together with their covariances.
Conversely, an analysis of the DES-SN5YR survey combined with BAO constraints strongly favoured ΛCDM within the procedure employed. Recent timescape analyses nevertheless contest the neutrality of that comparison, since the BAO extraction rested on an FLRW calibration and pipeline. This disagreement constitutes neither a validation nor a definitive refutation. It shows that testing the model requires a coherent chain running from the extraction of observables to the multi-probe comparison.
4. Confronting the observations
The Dark Energy Spectroscopic Instrument maps the three-dimensional distribution of millions of galaxies and quasars. Baryon acoustic oscillations serve as a standard ruler for reconstructing the evolution of distances at different epochs.
The cosmological results of DESI DR2 rest on more than fourteen million galaxies and quasars observed during the survey's first three years. The BAO measurements are well described by a flat ΛCDM model. The parameters favoured by the BAO nevertheless display a moderate tension with those inferred from the cosmic microwave background.
When the DESI data are combined with the cosmic microwave background, an evolving equation of state provides a better fit than ΛCDM within the w₀wₐ parameterisation. The preference reaches 3.1 σ. Adding different supernova compilations leads to values between 2.8 and 4.2 σ, depending on the sample used.
The parameterisation is written:
w(a) = w0 + wa(1 − a)
In ΛCDM, w₀ = −1 and wₐ = 0. The solutions favoured by certain combinations of data lie mainly in the region w₀ > −1 and wₐ < 0.
This description remains phenomenological. It indicates how the equation of state might evolve without identifying the mechanism responsible. Similar behaviour may come from a dynamic field, from an interaction in the dark sector, from a modification of gravitation or from an effective description influenced by inhomogeneities.
DESI provides no specific evidence in favour of cosmological backreaction. In certain combinations of data, the results put under tension the hypothesis that a fixed cosmological constant constitutes the definitive description, but they do not yet select a physical explanation. The dependence on the supernova compilation is a reminder of the weight of calibrations, selection effects and systematic uncertainties.
The dependence on supernova compilations does not come solely from sample size. It also depends on selection functions, bias corrections, models of intrinsic scatter, host-galaxy properties and photometric calibrations. A recent comparison of Pantheon+ and DES-SN5YR attributes much of a discussed offset between subsamples to differences in the modelling of intrinsic scatter, to estimates of host properties and to selection functions. These effects are incorporated, at different levels, into the uncertainty budgets. The persistence of a signal across several independent analysis chains remains a decisive criterion.
Crossing expansion and structure growth. Distance measurements describe the geometric history of expansion. They do not suffice to identify the mechanism producing it. Several models can reproduce similar distance–redshift relations while predicting a different evolution of matter.
Discrimination requires a joint analysis of several observables:
| Observable | Principal measurement | Discriminating role |
|---|---|---|
| H(z) | Expansion rate | Compares the expansion history between models. |
| Dₐ(z), Dₗ(z) | Angular and luminosity distances | Tests the geometry and the propagation of light. |
| fσ₈(z) | Growth of structures | Constrains the joint effect of expansion and gravitation. |
| Weak lensing | Projected matter distribution | Relates geometry to gravitational potentials. |
| Clusters and clustering | Abundance and clustering | Tests structure formation across several scales. |
A dynamic dark energy itself modifies growth by changing the expansion history. Some fields may also possess perturbations of their own. A modified gravitation may act directly on the relation between density and gravitational potential. Inhomogeneous models may finally modify the definition of distances, times and observables.
The separation between geometry and growth does not supply an automatic diagnostic. The relevant criterion is global coherence. A viable theory must explain, with one and the same set of parameters, the expansion, the distances, the growth, the lensing and the propagation of light.
f(R), scalar-tensor and DGP-type theories constitute distinct competitors. They modify the gravitational equations and attribute the acceleration to a dynamic different from that of averaging within unchanged general relativity. Their detailed analysis exceeds the scope of this synthesis. Their predictions must be compared with the same data sets.
The H₀ tension and environmental effects. The Hubble constant displays a persistent disagreement between several methods of inference. Within the ΛCDM framework, Planck's analysis of the cosmic microwave background gives:
| Planck + ΛCDM | H₀ = 67,4 ± 0,5 km·s⁻¹·Mpc⁻¹ |
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| SH0ES local distance ladder | H₀ = 73,04 ± 1,04 km·s⁻¹·Mpc⁻¹ |
This difference has led to an examination of the possible role of the local environment. An underdensity can produce outward-directed velocities and increase the apparent expansion rate measured at small distance.
Within ΛCDM, cosmic-variance analyses generally conclude that a plausible local void does not suffice to explain the whole discrepancy. A profile deep enough to resolve the tension would be hard to reconcile with the fluctuations normally expected and with other observations.
Void profiles deep enough to modify H₀ strongly are also constrained by cluster kinematics, notably by the kinematic Sunyaev–Zel'dovich effect, as well as by density maps and cosmic variance. An environmental dependence remains possible within a strongly reduced space, in particular for explanations resting on an extreme local void.
Lemaître–Tolman–Bondi models constitute another class of inhomogeneous cosmologies. They describe spherically symmetric dust geometries whose density and expansion rate may vary radially, and have often been mobilised to test the hypothesis of a large local void. They differ from timescape, which rests on a statistical partition between voids and bound regions without placing the observer at the centre of a spherical structure.
More general inhomogeneous models nevertheless do not reduce to that hypothesis. Timescape, for example, attributes apparent variations of the Hubble flow to differences between regions, to curvatures and to the calibration of clocks. These predictions must be tested through dependence on distance, on direction and on the three-dimensional distribution of matter.
The H₀ tension constitutes a testing ground for environmental effects, not an automatic confirmation of backreaction. A model must quantitatively relate the measured value to the local structure and recover the global dynamics on the scales where statistical homogeneity becomes relevant.
Gravitational sirens as a new distance scale. Mergers of compact objects offer an independent method for measuring cosmological distances. The shape and amplitude of a gravitational signal allow the luminosity distance of the source to be estimated. These events are called standard sirens.
The method does not depend on the distance ladder built from Cepheids and supernovae. It nevertheless requires information about the redshift, obtained through an electromagnetic counterpart, the identification of the host galaxy or a statistical analysis using galaxy catalogues.
In standard general relativity, the gravitational luminosity distance and the electromagnetic distance describe the same cosmological geometry, subject to effects related to the source, to lensing and to propagation conditions. Some theories of modified gravitation predict, by contrast, a different evolution of the amplitude of gravitational waves.
METHODOLOGICAL POINT Standard sirens do not by themselves directly test backreaction. Their strength comes from the comparison between gravitational distances, electromagnetic distances, spectral shifts and mapping of the matter traversed. |
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Peculiar velocities limit precision at small distance. Gravitational lensing introduces a scatter in gravitational distances as in electromagnetic ones. In the geometric-optics regime, the two messengers probe the same geometry. When the gravitational wavelength becomes comparable to the characteristic scales of the deflector, however, wave-optics effects such as diffraction and interference may appear. Inhomogeneities can also produce effects partly degenerate with certain signatures of non-standard propagation.
Combining sirens with supernovae, BAO, lensing and galaxy clustering will make it possible to check whether one and the same effective geometry coherently describes several messengers. Crossing them with weak-lensing maps could help distinguish an apparent modification of distances produced by inhomogeneous matter from a genuinely non-standard gravitational propagation. This possibility remains prospective. Such convergence will offer an independent test of models that modify the relation between structure, expansion and propagation.
5. The historical imprint of structures
The present structure of the Universe results from a cumulative evolution. Dense regions have undergone collapses, accretions, mergers and tidal interactions. Voids have expanded while matter was redistributed toward filaments and clusters. Initially weak perturbations produced a strongly differentiated organisation through gravitational instability.
This dependence on the past must not be called gravitational memory. In general relativity, that expression designates a precise effect associated with the passage of gravitational radiation. The most suitable term here is the historical imprint of non-linear dynamics.
The power spectrum describes the two-point correlations of the density field. It does not contain all the information produced by couplings between modes. The bispectrum and trispectrum probe higher-order correlations, sensitive to non-linearities, to interactions between scales and to departures from a Gaussian distribution.
These statistics do not reconstruct the whole history of a region. They preserve signatures of the processes that took part in its formation. Separate-universe methods likewise study how a large-scale perturbation modifies local growth and small structures.
The notion of history thus takes on a limited physical sense. The late state carries the consequences of earlier interactions and transformations, without constituting a functional memory comparable to that of the living.
Relativistic simulations. Classical cosmological simulations generally use a Newtonian gravitation embedded in an imposed cosmological background. This approach provides very precise results for much of structure formation.
Recent numerical developments make it possible to incorporate more relativistic effects. The gevolution code rests on a weak-field approximation of general relativity. It computes the metric degrees of freedom in the Poisson gauge and evolves the particles from the geodesic equations.
These tools serve to quantify relativistic contributions on large scales, the effects of massive neutrinos, certain extensions of gravitation, the construction of light cones and the propagation of photons through a structured Universe.
The inclusion of massive neutrinos also provides a useful sensitivity test. Their free streaming reduces the growth of fluctuations below scales depending on their mass and modifies the non-linear power spectrum as well as the halo mass function. Their influence on QD must nevertheless be computed within each averaging prescription. It does not constitute a universal bound on the amplitude of backreaction.
Relativistic simulations have not established the existence of a backreaction able to replace dark energy. Their contribution is methodological: they make it possible to compute the amplitude of the effects instead of inferring it from an analogy. They make possible the comparison between an average dynamic, the local geometry and the observables actually measured.
Present simulations must nevertheless contend with a difficulty of scale. Weak-field codes such as gevolution allow vast cosmological volumes to be treated and relativistic corrections to be computed, but they do not constitute an approximation-free solution of the whole Einstein dynamics from large scales down to galactic structures. Combining a complete relativistic geometry, a large spatial dynamic range and a resolution sufficient to represent non-linear processes remains a major numerical challenge.
Results from gevolution must be interpreted within its Poisson-gauge formulation and its weak-field approximation. They do not constitute a universal measure of QD, whose definition depends on the domain and the foliation. Light-cone computations offer a complementary approach by bringing the simulated geometry directly alongside the observables.
A systemic hypothesis does not advance because it seems coherent. It advances when it produces a computable amplitude, a distinct signature and a reproducible comparison with the data.
6. Turning the intuition into a falsifiable programme
The idea of an evolving cosmic organisation becomes a scientific programme when it is translated into mechanisms and tests. An operational formulation may be stated thus: the non-linear formation of structures contributes to the effective cosmic dynamics, or to the relation between that dynamics and the observations, in a measurable way insufficiently represented by a strict separation between homogeneous background and perturbations.
A counterfactual test could compare simulated ensembles with the same mean density and the same two-point power spectrum, but different phase correlations or higher-order statistics. A robust difference in the kinematical backreaction term, the average curvature, the light-cone distances or the growth would then supply a measure of the contribution associated with multi-scale organisation beyond two-point statistics alone.
This proposal requires at least five conditions.
| Level | Requirement |
|---|---|
| 1 | Define the variables, the domains, the foliation, the observers and the relation between local and global quantities. |
| 2 | Quantitatively predict H(z), the distances, the growth, the lensing and the structure statistics. |
| 3 | Compute the propagation of light and gravitational waves within the model's geometry. |
| 4 | Confront one and the same set of parameters with several independent probes, without reusing extractions that impose the competing geometry. |
| 5 | State negative controls and observations capable of invalidating the model. |
EXAMPLE OF REFUTATION In a scenario of irrotational dust without Λ, where backreaction must explain the acceleration on its own, Buchert's equation imposes: QD > 4πG⟨ρ⟩D that is QD / (8πG⟨ρ⟩D) > 1/2 during the interval in which äD > 0. If a joint reconstruction of H(z), of the distances, of the growth and of the lensing constrains this ratio below 1/2 over the relevant domain, this version of the mechanism is refuted. This threshold is not a universal bound. It holds for this precise scenario and illustrates the expected form of a quantitative negative control. |
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This grid imposes the same discipline on the standard model and on the alternatives. ΛCDM must not be exempted from scrutiny when tensions persist. An alternative proposal cannot be validated by its capacity to reformulate an anomaly alone.
The level of proof must follow a clear progression: conceptual coherence, mathematical definition, quantitative prediction, multi-probe validation, robustness to methods of analysis and explicit possibility of refutation.
7. Observational prospects
The next advances will depend less on an isolated anomaly than on the convergence between several families of measurement.
Euclid will confront cosmic geometry with the growth of structures through weak lensing, baryon acoustic oscillations and galaxy clustering. Combining shapes, positions and spectral shifts will make it possible to test whether the same parameters describe the distances, the distribution of matter and its evolution.
The LSST survey at the Vera C. Rubin Observatory, officially launched in June 2026, will follow the southern sky for ten years and should catalogue about twenty billion galaxies. Its measurements of lensing, clustering and variability will extend the tests of structure growth and statistical homogeneity. The Roman space telescope will bring complementary depth and resolution, useful for controlling several instrumental and astrophysical biases.
Ground-based gravitational-wave networks, next-generation detectors and the LISA mission will supply independent distances through standard sirens. Combining them with spectral shifts, galaxy maps, lensing and electromagnetic distances will make it possible to test whether one and the same effective geometry describes several messengers.
None of these probes will directly measure the kinematical backreaction term. Their contribution will consist in reducing the space of models able to reproduce jointly the expansion, the distances, the growth, the lensing and environmental effects.
8. Epistemological reach
Modern cosmology usually distinguishes the homogeneous background, which describes global evolution, from structures, treated as perturbations. This separation remains one of the most effective approximations in contemporary physics.
Inhomogeneous cosmology does not require its abandonment. It examines the possibility that the background is an effective geometry issuing from the averaging of a structured Universe, rather than an entirely independent level onto which structures would simply be superimposed. The passage from a structured Universe to an effective cosmological background is not a physically neutral operation. Its validity must be established for the observables and scales at which it is used.
Statistical homogeneity may remain an excellent approximation while leaving cumulative effects tied to regional differences of expansion, curvature or proper time. The debate concerns the causal weight of structures in the effective dynamics and in the construction of the observables.
Depending on the tracers, statistics and thresholds adopted, the transition to homogeneity is generally sought at scales of the order of several tens to a few hundred megaparsecs, with values often close to 100 h⁻¹ Mpc in some analyses. This range does not define a single physical boundary. Nor does the statistical homogeneity of the distribution guarantee that every dynamic contribution from smaller scales has become negligible.
This perspective does not turn the Universe into an organism. It proposes a more general principle: an emergent organisation can modify the global constraints and relations from which it pursues its evolution.
The formulation remains hypothetical as long as no discriminating amplitude is established. Its value lies in its capacity to organise tests relating matter, geometry, structure formation and the signals that reach us.
The analysis remains limited to classical general relativity and to late cosmic structuring. Quantum effects liable to modify the primordial phase belong to another theoretical regime and are not invoked here.
Synthesis. The Universe does not grow like an organism. Its expansion describes the evolution of the geometry of space-time. The motions of matter, the interactions between galaxies and the formation of structures do not suffice, in their ordinary form, to explain cosmic acceleration.
The initial intuition nevertheless reveals a real problem. Matter is not distributed within a passive framework. It influences the geometry, which in turn orients its evolution. Perturbations become voids, filaments and clusters. These structures modify the local distributions of curvature, expansion and proper time. The observations then result from signals that have crossed this organisation.
The homogeneous model gathers these dynamics into an average description whose effectiveness is solidly established. Cosmological backreaction examines the limits of that operation. Buchert's formalism shows that the variance of expansion rates and shear can produce effective terms. Timescape explores the possible consequences of regional differences of curvature and temporal calibration. DESI strengthens interest in descriptions in which the equation of state might evolve, without determining the physical origin of the signal.
Growth measurements, lensing, gravitational sirens and relativistic simulations will make it possible to distinguish the scenarios. A cosmic contribution of organisation can be retained only if it leaves a coherent signature in several observables and improves the explanation without displacing the inconsistencies onto other data sets.
CENTRAL CONCLUSION The progressive organisation of matter could take part in the effective evolution of the cosmos when emergent structures modify the relations between curvature, expansion, scales and conditions of observation. This proposal does not make the Universe a living being. It defines a physical hypothesis to be quantified and submitted to refutation. |
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The cosmological background might then represent the average form of a Universe whose matter and geometry evolve together. The validity of this perspective will depend on its capacity to produce distinct predictions, to survive several data sets and to accept explicit criteria of refutation.
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Status of the data. The article distinguishes established results, observational tensions and still open hypotheses. The numerical values and the state of the DESI results correspond to the publications available at the July 2026 revision. The examples of refutation remain limited to the assumptions proper to each scenario. The clarifications on supernovae, the cosmic microwave background, LTB models and massive neutrinos delimit the uncertainties without widening the theoretical scope.