1. The omega problem
There has always been a problem with the expanding universe.
Will it go on expanding forever?
The answer has depended on the balance between the initial expansion rate and the gravitational pull between the galaxies.
This is called the critical matter density of the universe(Ω)
If the pull of the galaxies is large enough. The galaxies will come to a stop and gravity will win. Pulling the galaxies back together in a big crunch.(Ω>1)

2. The omega problem
If the rate of acceleration is large enough the galaxies will continue to separate perhaps at a decreasing rate but they will drift apart leaving a cold empty hyper-large void ever increasing in size.(Ω<1)
These are called the open and the closed universe models.

3. The omega problem There is a third possibility:
The expansion rate could be exactly balanced with the gravitational attraction, leading to a situation where the gravitational pull is exactly balanced with the expansion. (Ω = 1)
For the universe to have existed for so long omega must be very close to 1.

6. Dark Energy Recent observations have caused a problem with this model.
The Hubble graph appears not so straight a line as it originally appeared. Closer galaxies are in fact accelerating slightly FASTER than expected.
The rate of expansion seems to be increasing!
This cannot be explained within traditional cosmology.
Something is continuing to accelerate the expansion of the universe.
We call this dark energy.

8. Cosmic Acceleration
The last few years of the twentieth century saw a revolution in cosmology, with the measurement of the acceleration term in expansion at high redshifts and the identification of dark energy as a major cosmological component. Supernovae are the prime yardstick for measuring the rate of expansion at moderate and high redshifts, but applying appropriate corrections for in situ reddening by dust remains an issue.