Calibrating the Standalone Detection Threshold of Cosmic Chronometers: A Monte Carlo Null-Sensitivity Test

Abstract We calibrate the intrinsic curvature-resolving power of Cosmic Chronometer (CC) measurements to determine their standalone sensitivity to late-time cosmic acceleration. Treating the current CC compilation (N=31, 0 < z < 2) as a differential curvature detector, we perform Monte Carlo simulations under a fiducial ΛCDM cosmology and evaluate its response against a constant-expansion null boundary (a ∝ t). We find that for current observational uncertainties, the dataset yields ΔBIC ≈ -1.4, indicating that the signal of acceleration lies below the standalone detection threshold of the probe. We quantify this limitation by measuring a false-preference rate of ~40%, defined as the frequency with which noise mimics a non-accelerating universe. We conclude that while CC data are fully consistent with the standard model, they currently operate in a degeneracy regime where differential measurements alone cannot independently resolve the transition to acceleration. We forecast that reducing fractional H(z) uncertainties by a factor of ~2–3 is required to cross the threshold for decisive standalone detection. Code Availability The Python analysis pipeline used for this calibration is available at: https://github.com/XDaGee8/cosmic-chronometers-sensitivity