Model-independent late-universe measurements of $H_0$ and $Ω_\mathrm{K}$ with the PAge-improved inverse distance ladder

TL;DR

This work develops a model-independent inverse distance ladder using PAge and MAPAge to jointly constrain the Hubble constant $H_0$ and spatial curvature $Ω_{ m K}$ from late-time data. By combining DESI DR2 BAO, DESY5 SN, SGL, CC, and GRB distances, the authors obtain precise $H_0$ measurements and find $Ω_{ m K}$ consistent with zero within $1σ$ for the PAge and MAPAge parameterizations, while ΛCDM with curvature shows a mild positive curvature preference with some data combinations. Bayesian model comparison consistently favors PAge and MAPAge over ΛCDM, with MAPAge offering stronger late-time evidence; curvature tension largely disappears in the model-independent approach. The results imply that current late-universe data support a flat universe in a model-independent framework and highlight the value of PAge/MAPAge for robust, cosmology-agnostic inferences of $H_0$ and $Ω_{ m K}$, with future surveys poised to further improve precision.

Abstract

The standard $Λ{\rm CDM}$ model has encountered serious challenges and the $H_0$ tension has become more significant with increasingly precise cosmological observation. Meanwhile, inconsistencies in measurements of the curvature parameter $Ω_\mathrm{K}$ between different datasets also have emerged. In this work, we employ two global and cosmic age-based parameterizations, PAge and MAPAge, to perform model-independent measurements of the Hubble constant $H_0$ and $Ω_\mathrm{K}$ by utilizing the inverse distance ladder (IDL). To construct the PAge-improved IDL, we utilize the strong gravitational lensing (SGL), cosmic chronometers (CC), and gamma ray bursts (GRB) data to calibrate the latest DESI DR2 baryon acoustic oscillation data and DESY5 type Ia supernova data. Our analysis indicate that DESI+DESY5+SGL+CC+GRB gives $H_0=71.59\pm 0.94\,{\rm km}~{\rm s}^{-1}~{\rm Mpc}^{-1}$ in the MAPAge model, reducing the $H_0$ tension to the $1.0σ$ level. Extending to MAPAge$+Ω_{\rm K}$ model, we obtain $Ω_\mathrm{K}=0.001\pm 0.038$, which suggests that current late-time data are consistent with a flat universe. Finally, the Bayesian analysis indicates that the present late-universe data provide weak to moderate evidence in favor of PAge and MAPAge relative to $Λ{\rm CDM}$.

Figures (2)

• Figure 1: The whisker plot of $H_0$ in the $\Lambda$CDM, PAge, MAPAge, $\Lambda\mathrm{CDM}+\Omega_{\rm K}$, PAge$+\Omega_{\rm K}$, and MAPAge$+\Omega_{\rm K}$ models using the DESI, DESY5, SGL, CC, and GRB data. Here, for $H_0$ we calculate the tension with SH0ES, while for $\Omega_{\rm K}$ we assess its deviation from zero.
• Figure 2: The logarithmic Bayes factors ($\ln\mathcal{B}_{ij}$) obtained from the DESI, DESY5, SGL, CC, and GRB data, where $i$ denotes the PAge, MAPAge, PAge$+\Omega_{\rm K}$, and MAPAge$+\Omega_{\rm K}$ models and $j$ is the $\Lambda$CDM model.