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

Abstract

Inferring high-fidelity constraints on the spatial curvature parameter, ${\Omega }_{\mathrm{K}}$, under as few assumptions as possible, is of fundamental importance in cosmology. We propose a method to non-parametrically infer ${\Omega }_{\mathrm{K}}$ 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 ${\Omega }_{\mathrm{K}}$ 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 ${\Omega }_{\mathrm{K}}=-0.03\pm 0.26$, 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 ${\Omega }_{\mathrm{K}}$ at the $\mathcal{O}(10^{-2})$ level.

5 pages, 2 figures, to be submitted to MNRAS letters. Comments welcome! Code available at: https://github.com/sdhawan21/Curvature_GP_LateTime