Thanks for the question Harriet,
The universe is expanding at an accelerated rate. There are several pieces of evidence, but the simplest one comes from comparing the distance to stars with the rate at which they're moving away from us. If (for a fixed time from the start) the distance were just a constant times the velocity, that would fit a simple picture where each object has been moving away from us at its own fixed rate.
We actually have very good measures of how fast stars were moving away from us when the emitted the light we're now seeing. The frequencies of the special colors emitted by atoms shift depending on that rate (the Doppler shift), and those can be measured accurately.
The hard part is to figure out how far away the star was when it emitted the light we're now seeing. Astronomers determine this using the brightness of stars called 'standard candles', especially type 1a supernovas. These supernovas emit about the same amount of light, and the differences from the average correlate well with the lifetime of the supernova's initial bright period. Since that's measured, a good estimate of the light emission can be obtained. Then how bright it is tells us how far away it was.
The plot of distance versus velocity doesn't quite fit the no-acceleration picture. It looks like in the first few billion years the expansion was slowing down, but for the last few billion it's been speeding up.
-Zach and mbw
(published on 12/12/2009)