Invited Review given at the 18th Texas Symposium held in
Chicago,
December 1996. To be published by *World Scientific Press*, eds. A.
Olinto, J. Frieman, and D. Schramm.
For a PDF version of the article, click
here.

## MEASURING COSMOLOGICAL PARAMETERS

### Wendy L. Freedman

Carnegie Observatories,
813 Santa Barbara St., Pasadena, CA 91101

**ABSTRACT.** In this review, the status of
measurements of the matter density
(Ω_{m}), the vacuum
energy density or cosmological constant
(Ω_{Λ}), the Hubble
constant (*H*_{0}), and ages of the
oldest measured objects (*t*_{0}) are
summarized. Measurements of the
statistics of gravitational lenses and strong gravitational lensing
are discussed in the context of limits on
Ω_{Λ}.
Three
separate routes to the Hubble constant are considered: the measurement
of time delays in multiply-imaged quasars, the Sunyaev-Zel'dovich
effect in clusters, and Cepheid-based extragalactic distances.
Globular-cluster ages plus a new age measurement based on radioactive
dating of thorium in a metal-poor star are briefly summarized. Limits
on the product of *H*_{0} *t*_{0} are also
discussed. Many recent,
independent dynamical measurements are yielding a low value for the
matter density
(Ω_{m} ~
0.2-0.3). A wide range of Hubble
constant measurements appear to be converging in the range of 60-80
km/sec/Mpc. Areas where future improvements are likely to be made
soon are highlighted; in particular, measurements of anisotropies in
the cosmic microwave background. Particular attention is paid to
sources of systematic error and the assumptions that underlie many of
the measurement methods.

**Table of Contents**

- INTRODUCTION

- Ω
_{m} - THE MATTER DENSITY
- Galaxies and Clusters: Dynamical Measures &
Mass-to-Light Ratios
- Dynamics of the Local Group
- Cluster Baryon Fraction
- Peculiar Velocities: Density and Velocity
Comparisons
- Galaxy Pairwise Velocities

- Ω
_{Λ}
AND Ω_{m} LIMITS
- Gravitational Lens Statistics
- Strong Gravitational Lenses
- Ω
_{m} and
Ω_{Λ} from Type Ia Supernovae

- SUMMARY OF CURRENT Ω
_{m} AND
Ω_{Λ} MEASUREMENTS

- H
_{0} - THE HUBBLE CONSTANT
- "Physical" versus "Astronomical"
Methods
- Gravitational Lenses
- Sunyaev Zel'dovich
Effect and X-Ray Measurements
- The Cepheid-Calibrated Extragalactic Distance
Scale

- t
_{0} - AGES OF THE OLDEST STARS
- Globular Cluster Ages
- Thorium Ages

- REMAINING ISSUES FOR MEASURING t
_{0}

- H
_{0} t_{0}

- COSMOLOGICAL PARAMETERS FROM COSMIC MICROWAVE
BACKGROUND ANISOTROPIES

- SUMMARY

- REFERENCES