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

TL;DR

This work develops a model-independent framework to constrain the SNIa absolute magnitude $M$, the curvature $Ω_k$, and the BAO sound horizon $r_d$ by combining cosmic chronometers with SNIa and BAO data and reconstructing the expansion history $H(z)$ through Gaussian Processes. By jointly analyzing $M$, $Ω_k$, and $r_d$ with current DESY5 SNIa and DESI DR2 BAO (and CCH), the authors find results compatible with a flat universe at about $1.7σ$, with $M\approx -19.324$, $Ω_k\approx -0.143$, and $r_d\approx 144$ Mpc, yielding $H_0\approx 68.8$ km s$^{-1}$ Mpc$^{-1}$. They also explore the impact of replacing DESI data with 2D/angular BAO and Pantheon+ SNIa, observing shifts in $H_0$ and tighter curvature constraints when higher-redshift SNIa are included. A first forecast for future data (LSST, Euclid, WST/ATLAS, DESI) indicates substantial improvements: $\sigma_M$ could drop by ~54% and $\sigma_{r_d}$ by ~66%, enabling $\sim2\%$ determinations of $H_0$ and ~50% gains in $Ω_k$ precision, while controlling a small GP-induced reconstruction bias. Overall, the results demonstrate the feasibility and value of a model-independent approach to tighten key cosmological calibrators and geometry tests in the coming decade.

Abstract

Model-independent approaches have gained increasing attention as powerful tools to investigate persistent tensions between cosmological observations and the predictions of $Λ$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, $Ω_k$, using CCH with DESY5 and DESI DR1/DR2. We find this data combination compatible with a flat universe at $\sim1.7σ$, with $Ω_k=-0.143\pm0.085$, 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 $(M,Ω_k,r_d)$, 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 $Ω_k$ 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]

Figures (3)

• Figure 1: Two-dimensional contour plots in all the planes of the parameter space $(M, \Omega_k, r_d)$ and the corresponding one-dimensional posterior probability distributions obtained from the analyses described in Sec. \ref{['sec:res_curr']}. The 2D contours are evaluated at 68% and 95% C.L.
• Figure 4: Percentage improvement factor on the parameters studied in this work ($x$-axis) achieved by future surveys in the pessimistic and optimistic scenarios for CCH$^{*}$+LSST-Y10+DESI$^{*}$ analyses. This is computed over the results obtained with the most recent available data, CCH+DESY5+DESI DR2.
• Figure 5: Example of the application of the skewed-normal fit (solid lines) on the noisy posteriors (dashed lines) for $M$ and $\Omega_k$ from the 2D joint analysis with LSST$_{\rm opt}$ + CCH$^{*}_{\rm pes}$. In this case, we obtain $\alpha_M = -1.09$ and $\alpha_{\Omega_k} = 1.16$.