Testing the Structure Growth Predictions of the Order Parameter Spacetime Theory with DESI DR1 Full-Shape Galaxy Clustering

Abstract

We test the structure growth predictions of the Order Parameter Spacetime Theory using DESI DR1 full-shape galaxy clustering measurements. The theory derives the dark energy equation of state from first principles via the information–Einstein equations, w(z) = −1 − (α/3)·[c₀(1+z)^{−α}/(1−c₀(1+z)^{−α})], controlled by two physical parameters: the present-day feedback coefficient c₀ and the redshift evolution index α. We fit the compressed ShapeFit parameters (D_V/r_d, D_H/D_M, fσ_s8, m) in six redshift bins (z = 0.30–1.49) provided by the DESI DR1 full-shape analysis, totaling 24 data points. The best-fit χ² = 28.08 for 20 degrees of freedom, with reduced χ² = 1.40, yields H₀ = 70.14 km/s/Mpc, Ω_m = 0.280, c₀ = 0.000, and α = 0.904. Compared to the ΛCDM model (χ² = 28.08), Δχ² = 0. The feedback coefficient c₀ is driven to zero by the data, indicating that the Order Parameter Spacetime Theory naturally reduces to its ΛCDM limit at the current level of precision, passing its first full-shape structure growth test. This null result is fully consistent with the theoretical prediction that the information dissipation tensor vanishes in the zero-temperature limit, Υ → 0. Combined with the independent test of the background expansion using DESI DR2 BAO and fσ₈ data, the theory has now passed its first tests at two independent levels — the expansion history and the growth of structure. The cross-validation of c₀ = 0 by two independent datasets greatly reduces the likelihood that this result is a statistical fluctuation or a systematic artifact. We discuss the prospects for future high-precision surveys (Euclid, DESI DR2) to detect a non-zero c₀.