What question did this study set out to answer?

This research aims to determine the cosmic expansion history and Hubble constant while minimizing theoretical assumptions.

June 23, 2026Open Access

The Hubble Constant from Symbolic Regression: Adversarially Validated with DESI DR2, M(z) Non-Evolution, and External Constraints

Key Points

This research aims to determine the cosmic expansion history and Hubble constant while minimizing theoretical assumptions.
Applied symbolic regression using PySR on various cosmic data sets including BAO and supernova samples.
Joint fitting yielded a polynomial model for H(z), determining H0 with data from DESI DR1/DR2 and other cosmic measurements.
Conducted an adversarial validation exercise with multiple challenges to test the robustness of findings.
H0 was determined to be 68.0 km/s/Mpc, consistent with prior measurements at 1.2 sigma.
Validation exercises confirmed robustness, with no fatal challenges affecting results.
Findings suggest the Hubble tension is linked to Cepheid calibration rather than the model of expansion history.

Abstract

We apply symbolic regression via PySR to cosmic chronometer (CC), BAO (SDSS + DESI DR1/DR2), and three independent supernova samples (Pantheon+ full covariance, DES-SN5YR, Union3) to discover the cosmic expansion history H (z) with minimal theoretical priors. The data-driven search independently converges on a 4-parameter polynomial form H (z) = H0 + A z (z-B) (z²+C) with f (0) =0. Joint fitting yields H0 = 68. 0 +/- 0. 8 km/s/Mpc (68% CL), consistent with Planck 2018 at 1. 2 sigma. DESI DR2 (factor-two improved precision) confirms the DR1 result with H0 unchanged at 68. 3. We test for evolution of the supernova absolute magnitude M (z), finding alpha = 0. 020 +/- 0. 010 consistent with zero. External constraints from GW170817, DES Y3+GW, and TDCOSMO 2025 lensing combine to H0=68. 8+/-2. 3. A direct LambdaCDM fit gives H0=67. 9, joint chi²=1429. 4 vs SR 1430. 6 (Delta chi²=1. 2). Fixing M to the SH0ES Cepheid calibration is rejected at Delta chi² = +52 to +82 (7-9 sigma). An adversarial validation exercise (2 rounds, 14 challenges, 10 partially sustained, 4 rejected, none fatal) confirms robustness. We conclude that the Hubble tension resides in the Cepheid calibration of M, not the expansion history shape; H0 approx 68 regardless of model choice, data combination, or adversarial scrutiny.

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