Expansion and critical density

The universe is expanding. The evidence is clear from viewing the doppler shift (called the red shift since the wavelength of visible light moves toward the red) of light from distant galaxies. The spectral lines of elements have their frequency reduced, and wavelength increased, due their relative motion away form Earth. The average velocity of a galaxy can be infered from the red shift. These velocities appear to rise linearly with the distance z from home.

The constant H is known as Hubble's constant. If we write the above equation as

we can see that H/c has units of inverse light-years. Observationally, the value of H/c is approximately 5 E-11 (l.y.-1), although the value is disputed to the 50% level. Thus, a galaxy is locate 108 light-years away, it is expected to be travelling with a velocity of 5.0 E-3 times the speed of light.

By asking the question "When would the distant galaxy and earth have been at the same point given they are currently separated by 108 light-years", one can calculate the age of the universe under the assumption that matter is coasting. This assumption neglects the fact that gravity is slowing down the expansion rate. But to within a factor of two, one can estimate that the age of the universe is close to 15 billion years. By tracing the trajectories of galaxies backwards in time, it appears that all matter originated from a given point in space and time. This is refered to as the big bang.

Gravity slows down the expansion, and if the universe has sufficient mass, will reverse the expansion and bring on the big crunch. The mass density required to stop the expansion is refered to as the critical mass density. Observationally, the universe appears to have approximately 5% of the necessary density, although various extrapolations disagree by more than a factor of two. By observing the rotation of galaxies, it also appears that there may be several times more matter in the galaxy, and perhaps more in the universe, than is contained in visible stars. This missing matter is refered to as dark matter, matter that does not radiate like that in stars. Exotic candidate theories abound to explain the nature of dark matter, and understanding the mass density of the universe is one of the great motivations to make improve astronomical measurements.

Examples     Cosmo/Astro index