Probing the Hubble Tension with an Infinite-Future Condition on the Hubble Parameter

We study the impact of imposing an infinite-future condition on Gaussian-process (GP) reconstructions of H ( z ) from 37 cosmic-chronometer measurements. Implementing the asymptotic limit H ( − 1 ) = 0 expected in constant- w CDM with w > − 1 as a pseudo-point at z = − 1 with tunable uncertainty σ − 1 lowers the GP-inferred Hubble constant from H 0 = 68.71 ± 6.08 to H 0 ≃ (64.67–65.86) ± (4.45– 4.85 ) k m s − 1 M p c − 1 . The resulting H 0 remains within ∼ 0.32–0.61 σ of the Planck ΛCDM value, while the separation from representative local distance-ladder measurements increases to ∼ 1.45–1.83 σ . A scan over σ − 1 shows that the shift is governed by the effective pseudo-point weight, interpolating between the hard-condition and data-dominated limits. Finally, constant- w CDM Markov Chain Monte Carlo (MCMC) fits to the same H ( z ) data with H 0 fixed to the GP-inferred values show that Ω m is only weakly affected, whereas lower H 0 shifts w toward less negative values; allowing curvature broadens constraints and remains consistent with Ω k = 0 .