The Fundamental Cosmological Parameters

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In the evolving Big Bang universe, Fate has a value that can be precisely determined. The universe may continue expanding forever or it may slow to a stop and begin contracting.

It is the amount of mass in the universe that controls this Fate. Gravity, always pulling matter together, slows the rate of expansion. The mass of the universe (hence its gravity) can be best determined by finding the average density of the universe, q. Since mass curves space, the average density is a measure of how curved space is. An open universe is negatively curved and will always continue expanding. A closed universe is positively curved and will eventually begin contracting. An interesting case occurs if the universe is uncurved (or "flat")--the rate of expansion will slow, and the radius of the universe will approach a fixed value.

The curvature is expressed by the value omega, the ratio of the q to q-critical (q-critical is the value that yields an uncurved universe.) If omega is less than one, the universe is open. If omega is greater than one, the universe is closed. If omega is exactly equal to one, the universe is "flat."

By looking at the matter we can see in the universe (galaxies) it appears that q is much less that q-critical. However, it also appears (through studying various gravitational effects such as the way galaxies rotate or the way galaxies orbit in clusters) that we can only see a small fraction of the mass in the universe. Furthermore, there are important theoretical reasons for believing that the universe expanded extremely rapidly for a period early in its history, and thus the curvature was driven to a value very close to zero. In other words, the universe became "flat."

The rate at which the universe is currently expanding is termed the Hubble Constant (Ho) after astronomer Edwin Hubble who first determined that distant galaxies are receding from one another (i.e. space is expanding) at a rate proportional to distance. This number is one of the most important numbers in cosmology because it can be used to estimate the size and age of the universe. However, obtaining a true value for Ho is very complicated. Astronomers need two measurements. First, spectroscopic observations reveal the galaxy's redshift, indicating its radial velocity (velocity along the line of sight or, in other words, away from our galaxy). The second measurement, the most difficult value to determine, is the galaxy's precise distance from earth. Reliable "distance indicators," such as variable stars and supernovae, must be found in galaxies. The value of Ho itself must be cautiously derived from a sample of galaxies that are far enough away that motions due to local gravitational influences are negligibly small.

The age of the universe can be determined directly from the Hubble constant. In an open universe, the age is given by one over Ho. In a closed universe, this number must be multiplied by 2/3. (A flat universe is a case where the universe is open--but just barely.).

There have been many attempts to determine Ho, and there is present agreement that the value is in the range of 45 to 90 kilometers per second per megaparsec. This translates into an age for the universe of between 10 to 20 billion years. In the previous issue of the Ascending Node, we reported on a survey of a distant galaxy which yielded a Ho value of around 80 to 90. A recent study of supernovae in distant galaxies yielded a result of around 75. These high values of Ho translate to the younger universe (around 11 billion years).

However, other surveys have returned a lesser value of Ho. Studies of gravitational lensing gave a result in the range of 50 to 60, implying an older universe. Gravitational lenses are a more direct way of analyzing Ho since you don't need an independent method to determine the distance.

The Big Bang theory (cosmologists call it "The Standard Model") has been amazingly successful, becoming stronger over the years as its predictions were verified. These include the existence of a very smooth, isotropic radiation pervading the universe (the Cosmic Background Radiation), and the raw abundance of hydrogen, helium, and lithium in the universe.

Another way to determine whether the universe is open or closed would to be to find out the density of matter very early in the universe, a parameter termed initial density, or qo. It turns out that deuterium production is extremely sensitive to density, so measuring the amount of deuterium in the universe would give qo. Unfortunately, the process of nucleosynthesis in stars destroys deuterium, so you might think making this measurement would be impossible. But, luckily, studies of quasar spectra show that there are pristine clouds of gas out there in intergalactic space. These clouds are being studied closely with HST and the new Keck telescope, studies which should pin down the value of qo. This is the golden age of astronomy. Our cosmology may be soon capped off with a keystone--the discovery of the age of the universe and the nature of its ultimate fate.

Guy McArthur