Model-independent constraints on $\Omega_m$ and $H(z)$ from the link between geometry and growth

TL;DR

This paper develops a model-independent method to constrain the Universe's expansion history and matter density using Gaussian processes and various cosmological data, showing compatibility with Planck 2018 and promising tighter future constraints.

Contribution

It introduces a novel, model-independent approach combining Gaussian processes with multiple data sets to constrain cosmological parameters without assuming a specific cosmological model.

Findings

Reconstructed expansion history aligns with Planck 2018 predictions.

Current data constrains H(z) to 9.4% precision on average.

Estimated matter density Omega_m = 0.224 ± 0.066, compatible with Planck.

Abstract

We constrain the expansion history of the Universe and the cosmological matter density fraction in a model-independent way by exclusively making use of the relationship between background and perturbations under a minimal set of assumptions. We do so by employing a Gaussian process to model the expansion history of the Universe from present time to the recombination era. The expansion history and the cosmological matter density are then constrained using recent measurements from cosmic chronometers, Type-Ia supernovae, baryon acoustic oscillations, and redshift-space distortion data. Our results show that the evolution in the reconstructed expansion history is compatible with the \textit{Planck} 2018 prediction at all redshifts. The current data considered in this study can constrain a Gaussian process on $H(z)$ to an average $9.4 \%$ precision across redshift. We find $\Omega_m = 0.224 \pm 0.066$, lower but statistically compatible with the \textit{Planck} 2018 cosmology. Finally, the combination of future DESI measurements with the CMB measurement considered in this work holds the promise of $8 \%$ average constraints on a model-independent expansion history as well as a five-fold tighter $\Omega_m$ constraint using the methodology developed in this work.