Non-parametric spatial curvature inference using late-universe cosmological probes

TL;DR

This paper introduces a non-parametric method using Gaussian Processes to infer the spatial curvature of the universe from late-Universe cosmological probes, avoiding assumptions about the expansion history.

Contribution

The authors develop a model-independent approach combining Cosmic Chronometers and Type Ia Supernovae data to constrain spatial curvature, insensitive to calibration and early-Universe assumptions.

Findings

Current data yields .03 b1 0.26 for .

Method is robust against calibration uncertainties.

Forecasts suggest future surveys can constrain .0 at the 1% level.

Abstract

Inferring high-fidelity constraints on the spatial curvature parameter, $\Omega_{\rm K}$, under as few assumptions as possible, is of fundamental importance in cosmology. We propose a method to non-parametrically infer $\Omega_{\rm K}$ from late-Universe probes alone. Using Gaussian Processes (GP) to reconstruct the expansion history, we combine Cosmic Chronometers (CC) and Type Ia Supernovae (SNe~Ia) data to infer constraints on curvature, marginalized over the expansion history, calibration of the CC and SNe~Ia data, and the GP hyper-parameters. The obtained constraints on $\Omega_{\rm K}$ are free from parametric model assumptions for the expansion history, and are insensitive to the overall calibration of both the CC and SNe~Ia data (being sensitive only to relative distances and expansion rates). Applying this method to \textit{Pantheon} SNe~Ia and the latest compilation of CCs, we find $\Omega_{\rm K} = -0.03 \pm 0.26$, consistent with spatial flatness at the $\mathcal{O}(10^{-1})$ level, and independent of any early-Universe probes. Applying our methodology to future Baryon Acoustic Oscillations and SNe~Ia data from upcoming Stage IV surveys, we forecast the ability to constrain $\Omega_{\rm K}$ at the $\mathcal{O}(10^{-2})$ level.