Revisiting model-independent constraints on spatial curvature and cosmic ladders calibration: updated and forecast analyses

Model-independent approaches have gained increasing attention as powerful tools to investigate persistent tensions between cosmological observations and the predictions of $\Lambda$CDM. Notably, recent DESY5 Type Ia Supernovae (SNIa) and DESI Baryon Acoustic Oscillation (BAO) data challenge the validity of the cosmological constant, and they remain in tension with SH0ES local distance ladder measurements under standard pre-recombination physics. Building on our previous work, MNRAS 523 (2023) 3, 3406-3422, we present a follow-up analysis of the model-independent calibration of the local and inverse distance ladders using cosmic chronometers (CCH) data and Gaussian Processes. We jointly constrain the SNIa absolute magnitude, $M$, the comoving sound horizon at the baryon-drag epoch, $r_d$, and the spatial curvature parameter, $\Omega_k$, using CCH with DESY5 and DESI DR1/DR2. We find this data combination compatible with a flat universe at $\sim1.7\sigma$, with $\Omega_k=-0.143\pm0.085$, showing weaker compatibility than with Pantheon+, while the ladder calibrators read $M=-19.324_{-0.095}^{+0.092}$ and $r_d=(144.00^{+5.38}_{-4.88}$) Mpc. Although current uncertainties limit the precision of our constraints and prevent us from arbitrating the Hubble tension, it is nevertheless instructive to explore the constraining power of our methodology with future SNIa, CCH, and BAO from surveys such as LSST, Euclid, and DESI. We present the first forecast analysis for the triad $(M,\Omega_k,r_d)$, finding that, in an optimistic scenario, upcoming data will improve agnostic constraints on $M$ by $\sim$54% and on $r_d$ by $\sim$66%, enabling a $\sim2$% determination of $H_0$. Precision on $\Omega_k$ will increase by $\sim50$%. Our analysis outlines which improvements in future data - whether in quality, quantity, or redshift coverage - are likely to most effectively tighten these constraints.[abridged]