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

Abstract In recent years, model-independent approaches have gained increasing attention as powerful tools to investigate persistent tensions between cosmological observations and the predictions of the standard ΛCDM model. Notably, recent data from the DESY5 Type Ia Supernovae (SNIa) sample and the latest Baryon Acoustic Oscillation (BAO) measurements from the DESI collaboration challenge the validity of the cosmological constant, and under the assumption of standard pre-recombination physics, they still remain in tension with the SH0ES local distance ladder measurements. Building on our previous work, Mon. Not. Roy. Astron. Soc. 523 (2023) 3, 3406-3422, we present a follow-up analysis of the model-independent calibration of both the local and inverse distance ladders using cosmic chronometers (CCH) data and the Gaussian Processes technique. We constrain the SNIa absolute magnitude, M, and the comoving sound horizon at the baryon-drag epoch, rd, while simultaneously deriving a measurement of the spatial curvature parameter, Ωk, using CCH with DESY5 and DESI DR1 and DR2 data releases. Our results show that this data combination is compatible with a flat universe at ∼1. 7σ, with Ωk = −0. 143 ± 0. 085, indicating a weaker compatibility than that observed with SNIa from Pantheon+, while the ladders calibrators read M=-19. 324-₀. ₀₉₅^+0. 092 and rd = (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 observations from surveys such as Vera C. Rubin Observatory - LSST, Euclid, and DESI. Thus, for the first time, we present a forecast analysis for the triad (M, Ωk, rd). Our results indicate that, in an optimistic scenario, upcoming data will improve agnostic constraints on the ladder calibrators - M by ∼54 %, rd by ∼66 % - which enable us to constrain the Hubble parameter, H0, at a 2 % level. Precision on Ωk will increase by 50~{\ per\ cent}. Our analysis outlines which improvements in future data – whether in quality, quantity, or redshift coverage – are likely to have the greatest impact on tightening these constraints.