Tracing the Evolution of ${\Omega }_m(z)$ over the Last 10 Billion Years with Non-parametric Methods

Abstract

We investigate the redshift evolution of the matter density parameter, ${\Omega }_m(z)$, using galaxy cluster gas mass fraction measurements combined with cosmic chronometer $H(z)$ data and type Ia supernova luminosity distances. This provides a non-parametric probe of the normalization of the cosmological matter sector, which plays a central role in current tensions involving weak lensing measurements, cluster abundance analyses, and the $S_8$ parameter. Using Gaussian Process regression, we reconstruct ${\Omega }_m(z)$ without assuming a parametric form for its evolution. The reconstructed evolution is consistent with the standard ${\rho }_m\propto (1+z{)}^3$ scaling predicted by the $\Lambda$CDM model. We obtain ${\Omega }_{m0}=0.296\pm 0.044$ from the 44-cluster sample, and ${\Omega }_{m0}=0.271\pm 0.016$, $0.253\pm 0.017$, and $0.210\pm 0.013$ for the 103-cluster compilation, depending on the adopted mass calibration. While the reconstructed ${\Omega }_m(z)$ evolution remains consistent with the expected $\Lambda$CDM behaviour, the inferred normalization of ${\Omega }_{m0}$ depends strongly on the adopted cluster mass calibration. Consequently, cluster mass calibration systematics constitute the dominant source of uncertainty in the inferred normalization of ${\Omega }_{m0}$, exceeding the statistical uncertainties of the non-parametric reconstruction.

Final version matching published version at Physics of the Dark Universe