Accelerating universe is a term for the idea that our universe is undergoing rapid expansion. In the late 1990s, observations of a type I supernova produced an unexpected result that the expansion of the universe appears to be accelerating. These observations appear more firm as new data has appeared. This means that the speed with which a distant galaxy recedes from us increases over time.
As this trend continues, there is the resultant inability to see any other galaxies any more. This new theory of the end of the Universe has been called the Big Rip.
The observation of an accelerating universe appears to present great problems for Dyson's eternal intelligence. He posited that our universe is decelerating. There may be that possibility if Hubble came to the wrong conclusion. He may have overlooked the effect of time.
The oldest light we can receive is extremely old. Its source is moving away from us faster than the sources that are not so old. The resulting logic in that case is that there is a deceleration, not acceleration of the expansion.