Structure-motivated phantom-crossing dark energy: joint constraints from DESI DR2, supernovae and growth

Manuscript and CSV data behind the figures and tables of Z. Xu (2026), Structure-motivated phantom-crossing dark energy: joint constraints from DESI DR2, supernovae and growth, Research Square preprint, doi:10.21203/rs.3.rs-11371459/v1. Contents. P03_revised.pdf (manuscript); csv/ (plotted series of every figure, the fit and comparison tables, and the recomputed results, with an index file INDEX.csv). Major findings (dark energy and structure growth): The dark-energy density follows ρDE = K⟨ap2⟩/G with K ≈ 4, where ⟨ap2⟩1/2 ≈ 10−10 m s−2 is the mass-weighted rms dark-matter particle acceleration, and its background law ρDE ∝ ⟨ap2⟩(D/D0)n is driven by the linear growth factor D. Matching the linear bulk flow to the nonlinear virial flow at their crossover, a* ≈ 0.64, gives a halo acceleration ac0 ≈ 0.16 cH0, close to Milgrom's a0. In its scale-free limit the law gives an equation of state linear in the growth rate f = d ln D/d ln a, w = −1 − (n/3)(f − f×), which stays bounded and crosses w = −1 where f = f×. Against DESI DR2 BAO, the DESI compressed CMB likelihood, Pantheon+ supernovae and SDSS growth rates, the structural law improves on ΛCDM by Δχ2 = −8.4 to −9.7 and on CPL by 0.6–1.9. Both structure-growth-tied families have higher Bayesian evidence than CPL and better predict supernovae withheld from the fit. 97–100% of posterior histories have w0 > −1 and a single density maximum at z ≈ 0.4–0.8; the exponent n is degenerate with the acceleration clock and the halo-assembly timing. The coupling is postulated, and all results are conditional on the compressed CMB likelihood and the acceleration calibration. Keywords: dark energy; dark matter; cosmology: theory; cosmological parameters; large-scale structure; DESI; growth rate.