Emergent Expansion Cosmology (EEC): A Thermodynamic Closure for the Backreaction Problem and its Background-Level Observational Confrontation

Thermodynamically motivated closure model for the Buchert backreaction equations of general relativity, in which late-time cosmic acceleration emerges from the non-equilibrium free energy of the matter distribution evaluated on a coarse-grained nonlinear scale.

In this framework, backreaction is linked to the variance of density fluctuations generated during gravitational collapse and structure formation, producing an effective contribution controlled by the statistics of the smoothed density field. A density-dependent stiffness function, motivated by halo-collapse statistics and non-equilibrium thermodynamics, naturally yields an effective equation of state consistent with w = −1 at a characteristic density scale, without requiring a cosmological constant or additional dynamical fields.

The model is formulated in terms of a non-equilibrium free-energy density and an associated stiffness function that govern the coupling between matter inhomogeneities and the effective large-scale dynamics. The framework preserves the background Bianchi identity and is consistent with the second law of thermodynamics during epochs of active structure formation.

At linear perturbation order, the model introduces no additional propagating degrees of freedom. Instead, it produces a modified effective gravitational coupling in the growth sector, while maintaining vanishing gravitational slip, with Φ = Ψ.

By fixing the characteristic density scale using the observed epoch of peak halo formation, the model reduces to three free cosmological parameters, matching the parameter count of spatially flat ΛCDM.

A joint observational analysis using Pantheon+ Type Ia supernovae, BOSS DR12 BAO and growth-rate measurements, DESI DR1 BAO, and the model-independent Planck acoustic scale yields:

Ho = 70.77 ± 0.31 km s⁻¹ Mpc⁻¹
S8 = 0.754 ± 0.036
Ωm= 0.3189 ± 0.0045
Ωneq = 0.6810 ± 0.0045

The predicted S₈ value is consistent with weak-lensing surveys at the level of approximately 0.2σ, providing strong agreement with current low-redshift structure-growth constraints and significantly reducing the standard ΛCDM growth tension. The inferred Hubble constant lies between the Planck and SH0ES determinations, without requiring explicit tuning of the expansion history.

A key consistency test is the CMB acoustic scale. The model predicts θ★ = 0.010411, which is consistent with the Planck measurement 0.010409 ± 0.000006 at +0.27σ. This resolves the 5.4σ tension present in v6, which originated from the use of a ΛCDM-geometry-dependent ωₘ prior that is incompatible with the EEC expansion history.

The best-fit statistic for the combined datasets is χ² = 1441.4 (χ²/dof = 0.903), compared to approximately χ² ≈ 1410 for ΛCDM. The Δχ² ≈ 32 reflects the observational cost of a physically distinct expansion history while maintaining the same number of cosmological parameters. Both models achieve statistically acceptable fits across all datasets.

The full numerical codebase is publicly available at:

https://github.com/ismailkhanmcs/EEC_Notebook