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

Abstract

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 ${\sigma }_{-1}$ lowers the GP-inferred Hubble constant from $H_0=68.71\pm 6.08$ to $H_0\simeq (64.67$--$65.86)\pm (4.45$--$4.85)\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$. The resulting $H_0$ remains within $\sim 0.32$--$0.61\sigma$ of the \textit{Planck} $\Lambda$CDM value, while the separation from representative local distance-ladder measurements increases to $\sim 1.45$--$1.83\sigma$. A scan over ${\sigma }_{-1}$ 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 ${\Omega }_m$ is only weakly affected, whereas lower $H_0$ shifts $w$ toward less negative values; allowing curvature broadens constraints and remains consistent with ${\Omega }_k=0$.

10 pages, 11+3 figures, Published in Physics Letters B, 879 (2026) 140607