[Paper Review] Global Constraints On Key Cosmological Parameters

Gary Steigman, Terry P. Walker+1 more|arXiv (Cornell University)|Dec 6, 2000

Cosmology and Gravitation Theories3 citations

TL;DR

This paper uses Type Ia supernova data, X-ray cluster baryon fractions, and Big Bang Nucleosynthesis (BBN) constraints to estimate key cosmological parameters, finding strong support for a flat universe dominated by dark energy (ΩΛ ≈ 0.7) and a baryon density (ΩBh² ≈ 0.02) consistent with low primordial deuterium abundance. The results reconcile baryon densities across high-redshift BBN, CMB, and low-redshift cluster observations, reinforcing the standard cosmological model.

ABSTRACT

Data from Type Ia supernovae, along with X-ray cluster estimates of the universal baryon fraction and Big Bang Nucleosynthesis (BBN) determinations of the baryon-to-photon ratio, are used to provide estimates of several global cosmological parameters at epochs near zero redshift. We show that our estimate of the present baryon density is in remarkably good agreement with that inferred from BBN at high redshift, provided the primordial abundance of deuterium is relatively low and the Universe is flat. We also compare these estimates to the baryon density at z = 1100 as inferred from the CMB angular power spectrum.

Motivation & Objective

• To estimate global cosmological parameters—particularly ΩM, ΩΛ, and ΩB—using observations independent of structure formation models or inflation theories.
• To test the consistency of baryon density estimates across different cosmological epochs: high-redshift BBN, CMB, and low-redshift X-ray clusters.
• To assess the viability of a flat universe with a non-zero cosmological constant using supernova magnitude-redshift data and baryon fraction constraints.
• To resolve tensions between high- and low-deuterium BBN predictions by comparing with SNIa and cluster data.
• To evaluate the shape parameter Γ and the age of the universe, testing for consistency with large-scale structure and stellar age constraints.

Proposed method

• Utilizes magnitude-redshift data from combined High-Z Supernova Search Team and Supernova Cosmology Project SNIa observations to constrain ΩM and ΩΛ.
• Applies X-ray cluster measurements of the baryon fraction (fB) to estimate the present-day baryon density (ΩB) independently of BBN or CMB.
• Imposes the flatness assumption (k=0) to break degeneracy between ΩM and ΩΛ, yielding precise constraints on both parameters.
• Compares BBN-predicted baryon densities (for low and high deuterium abundance) with SNIa + cluster-based estimates to test consistency.
• Uses the HST Key Project constraint on H0 to estimate the age of the universe (t0) and the shape parameter Γ.
• Performs likelihood analysis on cosmological parameters, reporting 68% and 95% confidence intervals for key values.

Experimental results

Research questions

• RQ1 Is the baryon density inferred from low-redshift X-ray clusters consistent with that predicted by Big Bang Nucleosynthesis at high redshift?
• RQ2 Does the combination of SNIa data and cluster baryon fractions support a flat universe with a non-zero cosmological constant?
• RQ3 How do different BBN-predicted deuterium abundances (low vs. high) affect the consistency of cosmological parameter estimates?
• RQ4 To what extent do the SNIa-based estimates of ΩM and ΩΛ agree with those derived from CMB anisotropy measurements?
• RQ5 What constraints do the data place on the age of the universe and the shape parameter Γ, and are they consistent with large-scale structure observations?

Key findings

• The SNIa data combined with X-ray cluster baryon fractions and the assumption of flatness yield ΩM = 0.28+0.08−0.07, consistent with a dark energy-dominated universe.
• A baryon density of ΩBh² ≈ 0.02 is favored, which aligns with BBN predictions for a low primordial deuterium abundance (η10 ≈ 5.1).
• The high-deuterium BBN case (η10 ≈ 1.7, ΩBh² ≈ 0.006) is inconsistent with both SNIa + cluster data and CMB results.
• The CMB-inferred baryon density (ΩBh² ≈ 0.03) is roughly consistent with the low-deuterium BBN and SNIa + cluster estimate, though on the high side by ~60%.
• The shape parameter Γ ≈ 0.2 is consistent with large-scale structure observations, while the high-deuterium case predicts Γ ≈ 0.05, which is too low.
• The age of the universe is estimated at t0 ≈ 13–14 Gyr, resolving the 'age problem' and consistent with stellar age constraints.