Dark energy that follows the growth of structure: replacing the cosmological constant with a parameter-free equation

Gravity has drawn matter into a cosmic web of galaxies and clusters, and dark energy now slows the growth of this web. We test whether the dark-energy density follows this growth, ρ_DE ∝ fD = dD/d ln a, the growth of structure per e-fold of expansion. The model has no parameter beyond those of flat ΛCDM. Its self-consistent solution crosses w = −1 at z = 0.45, where fD peaks. DESI baryon acoustic oscillations (BAO), combined with the cosmic microwave background (CMB) and type Ia supernovae (SNe), prefer a crossing of w = −1. We fit DESI DR2 BAO, four SN samples and four CMB likelihood combinations based on Planck and ACT DR6. The model fits better than ΛCDM in all 16 combinations, by Δχ² = 6.7 to 19.7. It fits as well as the w0wa parametrization, which has two more parameters. It thus reproduces the known preference of these data for an evolving dark energy with no free parameter. For Planck PR4 CamSpec with the DES five-year SNe (DESY5), the Bayes factor against w0wa is ln B = 5.6. A conservative correction for our search over 55 forms lowers it to 1.6. A test of this search, fixed after we had found the model, gives p = 6×10⁻⁵ for these SNe; for Pantheon+ the preference stays below 3σ. Without SNe at z < 0.1, the preference for DESY5 drops from 19.7 to 7.2, consistent with the drop expected for a true fD model. The model raises the Hubble tension from 4.7σ to 5.6σ, and the S8 value from DES Y6 lowers its Δχ² against ΛCDM by 4.0. For DESY5-like data, the model projects near (w0, wa) = (−0.81, −0.65). We registered this point on 12 October 2026, and falsification criteria for future data on 12 and 14 October 2026. This record contains the paper (version 1). The reproduction package with the code, the best fits, the MCMC chains, all results used in the paper and the commands behind them is a separate record (DOI 10.5281/zenodo.23717715). The preregistration files are in three further records. All four records are linked under related works. This work was done mainly in collaboration with the AI system Claude (Anthropic). Occasionally we also used the OpenAI models GPT-6-Astra and GPT-6.1-Sol to comment on drafts and to suggest checks. The author is responsible for the content.