A model-independent treatment of cosmic ladder calibration and $\Omega_k$ measurement through low-$z$ observations

TL;DR

This paper introduces a model-independent approach to calibrate cosmic distance measures and estimate the curvature parameter using low-redshift observations, aiming to address the Hubble tension.

Contribution

It develops a Gaussian Processes-based method to reconstruct key cosmological parameters independently of CMB and early universe assumptions.

Findings

Estimated curvature parameter: Ω_k = -0.07^{+0.12}_{-0.15}

Measured absolute magnitude of SNIa: M ≈ -19.314 mag

Determined sound horizon at drag epoch: r_d ≈ 142.3 Mpc

Abstract

Looking at the well-known Hubble tension as a tension in the calibrators of the cosmic distance ladder, i.e. the absolute magnitude $M$ of standard candles such as supernovae of Type Ia (SNIa) and the standard ruler represented by the comoving sound horizon at the baryon-drag epoch, $r_d$, we propose a model-independent method to measure these distance calibrators independently from the cosmic microwave background and the first rungs of the direct distance ladder. To do so, we leverage state-of-the-art data on cosmic chronometers (CCH), SNIa and baryon acoustic oscillations (BAO) from various galaxy surveys. Taking advantage of the Gaussian Processes Bayesian technique, we reconstruct $M(z)$, $\Omega_k(z)$ and $r_d(z)$ at $z\lesssim2$ and check that no significant statistical evolution is preferred at 68\% C.L. This allows us to treat them as constants and constrain them assuming the metric description of gravity, the cosmological principle and the validity of CCH as reliable cosmic clocks, and SNIa and BAO as optimal standard candles and standard rulers, respectively, but otherwise in a model-independent way. We obtain: $\Omega_k=-0.07^{+0.12}_{-0.15}$, $M=(-19.314^{+0.086}_{-0.108})$ mag and $r_d=(142.3\pm 5.3)$ Mpc. At present, the uncertainties derived are still too large to arbitrate the tension but this is bound to change in the near future with the advent of upcoming surveys and data.