Emergent Expansion Cosmology (EEC) is a thermodynamically motivated closure for the Buchert backreaction equations of general relativity, in which cosmic acceleration is associated with the non-equilibrium free energy of the matter distribution evaluated on a coarse-grained scale, rather than with a cosmological constant. The non-equilibrium free energy scales with the variance of cosmic structure, tying the onset of acceleration causally to structure formation. EEC v10 supersedes v9 with one addition and no changes to the fit: the late-time fixed point of the coupled growth-expansion system, previously established only qualitatively, is now obtained in closed form. The attractor values are f* = (sqrt (73) - 1) /12, approximately 0. 629, wₑff* = (1 - sqrt (73) ) /9, approximately -0. 838, and q* = 2/3 - sqrt (73) /6, approximately -0. 757, with the Hubble rate H approaching zero while the universe continues to accelerate, and no asymptotic de Sitter state. These values are parameter-free consequences of the closure, independent of the coupling beta, of sigma₈, and of the initial amplitude of the non-equilibrium sector, verified numerically to better than 2 times 10^-5 for beta in the range 4 to 66. This sharpens the status of the present-day amplitude: the trajectory Omegaₙeq (a) and its endpoint are derived; only the trajectory's normalization is boundary data, fixed by flatness as in v9. The smoothing scale at which the internal variable is evaluated remains anchored to the nonlinearity scale of the matter field, fixed by the primordial spectrum and the matter density rather than chosen, as introduced in v9. The coupling is denoted beta throughout, consistent with the released code. The fit, datasets, and all numerical results are unchanged from v9 and v8. Confrontation with Pantheon+ Type Ia supernovae, BOSS DR12 BAO and growth-rate data, DESI DR1 BAO, and the model-independent Planck acoustic scale thetaₛtar (evaluated self-consistently within EEC geometry) yields H0 = 68. 56 +/- 0. 28 km/s/Mpc, sigma₈ = 0. 733, S8 = 0. 764, Omegaₘ = 0. 326, and Omegaₙeq = 0. 674, with a best-fit chi-squared approximately 1411. 8, statistically equivalent to LambdaCDM at equal parameter count. The predicted CMB acoustic scale matches Planck at +0. 01 sigma, and S8 (obtained without any weak-lensing likelihood in the fit) coincides with the value preferred by weak-lensing surveys. The inferred H0 sits on the Planck side of the distribution; the framework does not address the Hubble tension. The amplitude of the non-equilibrium sector is fixed by spatial flatness. While dimensionally natural, an order-unity coupling times H squared, with no 10¹20 vacuum-energy hierarchy, its derivation from first principles is not achieved here and is stated explicitly as the central open problem of the framework. With the v10 attractor, the present amplitude is understood as a position along a derived universal trajectory whose normalization remains external boundary data, sharpening but not resolving this open problem. EEC v10 is therefore presented as a falsifiable, LambdaCDM-equivalent closure with distinctive predictions: a redshift-dependent wₑff = - (4/3) f (z), a modified growth coupling mu (z), exactly vanishing gravitational slip eta = 0, an acceleration causally tied to structure growth, and a parameter-free late-time attractor distinct from the LambdaCDM de Sitter endpoint, rather than as a complete account of the origin of cosmic acceleration. The full numerical codebase is publicly available at: https: //github. com/ismailkhanmcs/EECNotebook
Ismail Khan (Fri,) studied this question.