Torsion-Born Early Dark Energy with an Onset Locked to Matter–Radiation Equality: Derivation and Pre-Registered Likelihood Tests
Year: 2026
Type: preprint
Abstract: Promoting the Barbero–Immirzi parameter of Einstein–Cartan–Holst gravity to a field gives a canonical, ghost-free pseudoscalar. With an assumed potential V = Λ⁴[1 − cos(φ/F)]³ it is axion-like early dark energy (EDE); we fix the peak of its energy fraction at matter–radiation equality, leaving two extra parameters, and test it with full Boltzmann codes and decision rules hashed before each fit. On Planck + ACT DR6 + DESI DR2 + Pantheon+ it improves on ΛCDM by Δχ² = −7.23; on SPT-3G D1 alone no version improves meaningfully (best Δχ² = −1.27). On all three CMB data sets combined with DESI DR2 and Pantheon+ it passes its pre-registered rule (Δχ² = −5.63, f_EDE = 0.070, H₀ = 70.15), but late evolving dark energy (w₀–wₐ) fits better (Δχ² = −10.89). A profile likelihood prefers f_EDE ≈ 0.05–0.10 (68%), but after a look-elsewhere correction for the initial angle the global significance is only 1.2–1.4σ, a weak hint. Fitted together with late dark energy, early energy improves χ² by 3.65 but does not pay for its two parameters. The favoured flat-bottomed n = 3 shape is not produced by the Nieh–Yan term or by natural instanton or anomaly potentials, and the equality lock cannot be derived from the minimal action. Two codes agree to 0.4 in χ². Acting late with its natural n = 1 potential, on code corrected for two AxiCLASS bugs we found, the field ties ΛCDM with Pantheon+, gains a weak, sample-dependent Δχ² = −6.2 with DES Y5, and never beats w₀–wₐ. The torsion-natural dark-matter coupling is excluded, and the minimal field cannot produce the measured cosmic birefringence. We state which parts are derived, which are assumed, and which failed. Version 3 (results final, 2 November 2026). Every n = 1 test was rerun on corrected AxiCLASS under a pre-registered replication rule (two bugs found by a null test: for n = 1 the field is forced into δ_m, and halofit/HMcode count the field as matter; a 10-second reproducer is included). Also new: a pre-registered birefringence test (the minimal field is excluded; with one added photon coefficient the late field predicts a reionisation-to-recombination rotation ratio R = 0.997, open for LiteBIRD), an S8 check on the corrected code, a laboratory spin bound, and exploratory ratio-pattern tests (not supported). Completed locked SF comparisons give Δχ² versus LCDM of −9.2245, −11.4405, and −12.8812 for Pantheon+, DES-Dovekie, and Union3; the locked rules classify all three as BEATS LCDM and COMPETITIVE (not BEATS) w0–wa, with Δχ² versus w0–wa of +0.7326, +1.7962, and +2.1152. Original and cold SF logs show all four minima flagged True and successful completion, with spread warnings remaining. SR-B2 classifies Pantheon+ (r=0.1053) and DES-Dovekie (r=0.2643) as DESI-driven and Union3 (r=0.3622) as partly DESI-driven; SR-R3 cold-start minima are stable for all three. The locked DES Y5 torsion-F test disfavors F1 (D_F=2.0917, G_F=−5.3328) and F2 (D_F=1.2706, G_F=−6.1539). These saved-fit comparisons are not independent cosmological evidence or a torsion detection and do not close the physical derivation: the supplied action still does not derive the assumed potential, compactness, N=9, or equality trigger. See the attached results-update PDF. Everything (code, every fit output, pre-registrations with SHA-256 hashes and lock times, a 10-minute reviewer guide, a script that recomputes the paper's numbers from the fit files, and the exact environment) is public at github.com/dannyeldridge54/the-twist-torsion-cosmology. ancillary_v3.zip holds the code, fit outputs and pre-registration files.
Author: Eldridge, Danny Lee
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224793366