For supernovae at redshift less than around 0.1, or light travel time less than 10% of the age of the universe, this gives a nearly linear distance–redshift relation due to Hubble's law. At larger distances, since the expansion rate of the universe has changed over time, the distance-redshift relation deviates from linearity, and this deviation depends on how the expansion rate has changed over time. The full calculation requires integration of the Friedmann equation, but a simple derivation can be given as follows: the redshift z directly gives the cosmic scale factor at the time the supernova exploded.

So a supernova with a measured redshift z = 0.5 implies the universe was 1/1 + 0.5 = 2/3 of its present size when the supernova exploded. In an accelerating universe, the universe was expanding more slowly in the past than it is today, which means it took a longer time to expand from two thirds its present size to its present size compared to a non-accelerating universe. This results in a larger light-travel time, larger distance and fainter supernovae, which corresponds to the actual observations. Adam Riess found that "the distances of the high-redshift SNe Ia were, on average, 10% to 15% farther than expected in a low mass density ΩM = 0.2 universe without a cosmological constant" This means that the measured high-redshift distances were too large, compared to nearby ones, for a decelerating universe.

As the universe gets older, the speed at which it’s expanding continues to raise and raise, thanks to a force called dark energy. Dark energy is a force that repels gravity, pushing the universe outwards, growing stronger as time goes on (Dark Matter and Dark Energy). This growth in strength is the event that causes the outwards expansion of the universe to accelerate with time. But once the universe ceases to expand any further, what’s going to happen? Will what remains just stay the same size for eternity? Scientists have guessed that, upon running out of dark energy to push the universe outwards, the universe will then begin to contract in upon itself, resulting in an event currently known to scientists as the “Big Crunch.” It was named this because it will be the crunching together of the entire universe, and thus the opposite of the Big Bang. All the matter in the universe will be condensed into one point, just like how it all started. Perhaps the cycle of the universe will restart: Big Bang, creation of the universe, expansion, contraction, Big Crunch, repeat. Although, the universe might never run out of dark energy to keep it expanding, faster and faster. There’s no way to know for sure until the time comes, and humans most likely won’t be there to see that happen. 

The universe’s expansion is accelerating due to a mysterious force known as dark energy. This force repels gravity, pushing all the matter in the universe outwards. Dark energy gets stronger as time goes on, causing the acceleration itself. The dark energy takes up 70% of the universe, with dark matter taking up 25% and the observable universe taking up the remaining 5%. That small portion of the universe, that twentieth that’s visible to humans, is so seemingly vast to humanity, but in comparison to the remaining 95%, what people could see is a minute amount. There’s just so much dark energy that the expansion of the universe will almost definitely continue to accelerate long after humanity- and the solar system- have been wiped from the universe.