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Tracing the Evolution of $Ω_m(z)$ over the Last 10 Billion Years with Non-parametric Methods

R. F. L. Holanda, J. F. Jesus, Z. C. Santana, R. C. Nunes

Abstract

We investigate the redshift evolution of the matter density parameter, $Ω_m(z)$, using galaxy cluster gas mass fraction measurements combined with cosmic chronometer $H(z)$ data and type Ia supernova luminosity distances. Our approach employs Gaussian Process Regression to reconstruct $Ω_m(z)$ in a non-parametric way, remaining only weakly dependent on a specific background cosmology. The reconstructed evolution is consistent with the standard $ρ_m \propto (1+z)^3$ scaling predicted by the $Λ$CDM model. We obtain $Ω_{m0}=0.296 \pm 0.044$ from the 44-cluster sample, and $Ω_{m0}=0.271 \pm 0.016$, $0.253 \pm 0.017$, and $0.210 \pm 0.013$ for the 103-cluster compilation, depending on the assumed mass calibration. While $Ω_m(z)$ follows the expected redshift behaviour, the inferred value of $Ω_{m0}$ shows a strong dependence on the cluster mass calibration. Within this framework, mass bias emerges as the dominant source of uncertainty, exceeding statistical errors.

Tracing the Evolution of $Ω_m(z)$ over the Last 10 Billion Years with Non-parametric Methods

Abstract

We investigate the redshift evolution of the matter density parameter, , using galaxy cluster gas mass fraction measurements combined with cosmic chronometer data and type Ia supernova luminosity distances. Our approach employs Gaussian Process Regression to reconstruct in a non-parametric way, remaining only weakly dependent on a specific background cosmology. The reconstructed evolution is consistent with the standard scaling predicted by the CDM model. We obtain from the 44-cluster sample, and , , and for the 103-cluster compilation, depending on the assumed mass calibration. While follows the expected redshift behaviour, the inferred value of shows a strong dependence on the cluster mass calibration. Within this framework, mass bias emerges as the dominant source of uncertainty, exceeding statistical errors.

Paper Structure

This paper contains 6 sections, 11 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Data sets and Results
  4. Sample of 44 clusters
  5. Sample of 103 clusters
  6. Conclusion

Figures (5)

  • Figure 1: Gaussian Process reconstructions of cosmological observables. Left: $H(z)$ reconstructed from 32 cosmic chronometer measurements Moresco:2022phi. Right: luminosity distance $D_L(z)$ reconstructed from the binned Union3 dataset Rubin:2023jdq. Shaded regions represent the $1\sigma$ and $2\sigma$ confidence intervals.
  • Figure 2: Gas mass fraction ($f_{\rm gas}$) measurements for the cluster samples. The left panel corresponds to the 44-cluster sample, while the right panel shows the 103-cluster sample.
  • Figure 3: Reconstruction of the matter density parameter $\Omega_m(z)$ from the 44-cluster $f_{\rm gas}$ sample. The shaded regions represent the $1\sigma$ and $2\sigma$ confidence levels, and the dashed line corresponds to the $\Lambda$CDM prediction.
  • Figure 4: Reconstruction of $\Omega_m(z)$ from the 103-cluster $f_{\rm gas}$ sample for different mass calibration schemes. Top left: $K^{\mathrm{CCCP}}$. Top right: $K^{\mathrm{CLASH}}$. Bottom: $K^{\mathrm{CMB}}$.
  • Figure 5: One-dimensional posterior distributions of $\Omega_{m0}$ derived from Gaussian Process reconstructions of $\Omega_m(z)$, highlighting the impact of different cluster samples and mass calibration schemes.