To determine if the expansion rate of the universe is speeding up or slowing down over time, cosmologists make use of the finite velocity of light. It takes billions of years for light from a distant galaxy to reach the earth. Since the universe is expanding, the universe was smaller (galaxies were closer together) when light from a distant galaxy was emitted than it is today. If the expansion rate of the universe is speeding up, then the size of the universe increases more rapidly with time than if the expansion were slowing down. Using supernovae, we cannot quite measure the size of the universe versus time. Instead we can measure the size of the universe (at the time the star exploded) and the distance to the supernova. With the distance to the exploding supernova in hand, astronomers can use the value of the speed of light along with the theory of General Relativity to determine how long it took the light to reach the earth. This will then tell them the age of the universe when the supernova exploded.
To determine the distances to these stars, cosmologists use the fact that Type Ia supernovae are nearly "standard candles": exploding stars of this type all have nearly the same absolute brightness or luminosity when they reach their brightest phase. By comparing the apparent brightness of two supernovae, we can thus determine their relative distances. This is similar to using the apparent brightness of a carís headlights at night to estimate how far away it is: if one carís headlights appear four times brighter than another identical carís, then the first car must be half the distance to the second. Type Ia supernovae are the cosmic equivalent of cars with the same wattage of headlights.
To determine the second piece of the puzzle, the size of the universe at the time of explosion, astronomers use the spectrum of the emitted light to measure the redshift. When a supernova explodes, it emits light in the form of a wave. As the light wave travels towards the earth over billions of years, the universe continues to expand, stretching this traveling wave as it does. The more the universe has expanded between the explosion and when we see the light with our telescopes, the greater the increase in the wavelength of the light. The visible light with the longest wavelength is the color red, so this process of increasing wavelength of the light wave is referred to as "redshifting". (For additional information on redshifts in DES, click here.)
By studying the spectra of supernovae or of the galaxies in which they explode, we can infer the redshift due to the expansion. Comparing the redshift with the distance for a large number of supernovae, we can derive the history of the cosmic expansion rate. In 1998, such measurements were first reported for supernovae at large distances, those which exploded when the universe was only two-thirds its present size. These supernovae appeared about 25% fainter, that is, farther away, than expected, an effect attributed to the speed-up of cosmic expansion over the last several billion years.
The Dark Energy Survey will measure the brightness of around 3,000 supernovae. These supernovae are billions of light years distant from earth. When the most distant ones DES will study exploded, the universe was only about half as big as it is now.