Baryonic Acoustic Oscillations (BAO) involves measuring the spatial distribution of galaxies to determine the rate of growth of cosmic structure within the overall expansion of the universe. This comparison can in theory distinguish between the different forms of Dark Energy. The patterns of galaxy clustering contain information about how cosmic structure is amplified from initial small fluctuations. This clustering encodes a robust 'standard ruler' or 'average separation' between galaxies which could be used to map out the expansion history of the universe in a manner analogous to type Ia supernova 'standard candles'.
The nature of this standard ruler is a preference for pairs of galaxies to be separated by a co-moving distance of 150 Mpc. This favoured separation is an echo of sound waves which propagated 13.3 billion years ago through the plasma before the Cosmic Microwave Background epoch of recombination, about 380,000 years after the Big Bang.
These sound waves emanated from primordial dark matter halos, which launched spherical wavefronts driven by radiation pressure from the compressed plasma. These sound waves travelled rapidly in the early universe, covering a comoving distance of 150 Mpc between the Big Bang and the epoch of recombination.
This study of the Dark Energy sounds straightforward, but it's not. The problem is that the standard ruler we are using is very large. Hence it is necessary to observe large regions of space to produce galaxy redshift surveys that cover Giga-parsec volumes to make a precision measurement of the BAO signal.