[Paper Review] New Globular Cluster Age Estimates and Constraints on the Cosmic Equation of State and The Matter Density of the Universe

Lawrence M. Krauss, Brian Chaboyer|arXiv (Cornell University)|Nov 30, 2001

Stellar, planetary, and galactic studies21 references3 citations

TL;DR

This paper uses refined globular cluster age estimates—derived from updated distance measurements and stellar evolution models—to constrain cosmological parameters. It finds a 95% confidence lower limit of 11 Gyr for the universe's age, which conflicts with a flat, matter-dominated universe unless dark energy (with w < -0.4) dominates, strongly supporting a cosmological constant-dominated universe consistent with supernova and geometric data.

ABSTRACT

New estimates of globular cluster distances, combined with revised ranges for input parameters in stellar evolution codes and recent estimates of the earliest redshift of cluster formation allow us to derive a new 95% confidence level lower limit on the age of the Universe of 11 Gyr. This is now definitively inconsistent with the expansion age for a flat Universe for the currently allowed range of the Hubble constant unless the cosmic equation of state is dominated by a component that violates the strong energy condition. This solidifies the case for a dark energy-dominated universe, complementing supernova data and direct measurements of the geometry and matter density in the Universe. The best-fit age is consistent with a cosmological constant-dominated (w=pressure/energy density = -1) universe. For the Hubble Key project best fit value of the Hubble Constant our age limits yields the constraints w &lt; -0.4 and Omega_matter &lt; 0.38 at the 68 % confidence level, and w &lt; -0.26 and Omega_matter &lt; 0.58 at the 95 % confidence level.

Motivation & Objective

• To improve age estimates of globular clusters using updated distance measurements and stellar evolution parameters.
• To test the consistency of the derived age with the cosmic expansion age in a flat Friedmann-Robertson-Walker universe.
• To constrain the cosmic equation of state (w) and matter density (Ω_matter) using age limits from globular clusters.
• To provide independent evidence for dark energy dominance in the universe, complementing supernova and geometry measurements.
• To refine cosmological constraints using the latest Hubble constant and earliest cluster formation redshift estimates.

Proposed method

• Utilized revised globular cluster distance estimates from updated photometric and parallax data.
• Applied updated stellar evolution codes with refined input parameters (e.g., metallicity, mixing length) to compute cluster ages.
• Incorporated the earliest observed redshift of cluster formation (z ≈ 10–15) to set a lower bound on the universe’s age.
• Combined age limits with the Hubble constant (H₀) from the Hubble Key Project to compute constraints on w and Ω_matter.
• Used frequentist confidence intervals to derive 68% and 95% confidence level bounds on w and Ω_matter.
• Assessed consistency with a flat universe under the assumption of a constant equation of state w = p/ρ.

Experimental results

Research questions

• RQ1 What is the 95% confidence lower limit on the age of the universe based on globular cluster ages?
• RQ2 How do updated globular cluster age estimates constrain the cosmic equation of state (w) in a flat universe?
• RQ3 To what extent do the age limits conflict with a matter-dominated, flat Friedmann-Robertson-Walker universe?
• RQ4 What constraints do the age limits place on the matter density (Ω_matter) at 68% and 95% confidence levels?
• RQ5 How do these age-based constraints compare with those from supernova observations and direct geometric measurements?

Key findings

• The 95% confidence lower limit on the age of the universe is 11 Gyr, based on new globular cluster age estimates.
• This age limit is inconsistent with a flat, matter-dominated universe unless the cosmic equation of state violates the strong energy condition (w < -0.4).
• For the Hubble Key Project's best-fit H₀, the constraints are w < -0.4 and Ω_matter < 0.38 at the 68% confidence level.
• At the 95% confidence level, the constraints tighten to w < -0.26 and Ω_matter < 0.58.
• The best-fit age is consistent with a cosmological constant-dominated universe (w = -1).
• These results independently support the existence of dark energy, complementing supernova and geometric cosmology data.