analyzed the clustering of these galaxies by calculating a two-point correlation function on the data. The correlation function (ξ) is a function of comoving galaxy separation distance (s) and describes the probability that one galaxy will be found within a given distance of another. One would expect a high correlation of galaxies at small separation distances (due to the clumpy nature of galaxy formation) and a low correlation at large separation distances. The BAO signal would show up as a bump in the correlation function at a comoving separation equal to the sound horizon. This signal was detected by the SDSS team in 2005. SDSS confirmed the WMAP results that the sound horizon is ~ in today's universe. Detection in other galaxy surveys The 2dFGRS collaboration and the SDSS collaboration reported a detection of the BAO signal in the power spectrum at around the same time in 2005. Both teams are credited and recognized for the discovery by the community as evidenced by the 2014 Shaw Prize in Astronomy which was awarded to both groups. Since then, further detections have been reported in the 6dF Galaxy Survey (6dFGS) in 2011, WiggleZ in 2011 and BOSS in 2012. Dark energy formalism BAO constraints on dark energy parameters The BAO in the radial and transverse directions provide measurements of the Hubble parameter and angular diameter distance, respectively. The angular diameter distance and Hubble parameter can include different functions that explain dark energy behavior. These functions have two parameters w0 and w1 and one can constrain them with a chi-square technique. General relativity and dark energy In general relativity, the expansion of the universe is parametrized by a scale factor which is related to redshift: The Hubble parameter, , in terms of the scale factor is: where is the time-derivative of the scale factor. The Friedmann equations express the expansion of the universe in terms of Newton's gravitational constant, , the mean gauge pressure, , the Universe's density , the curvature, , and the cosmological constant, : Observational evidence of the acceleration of the universe implies that (at present time) . Therefore, the following are possible explanations: The universe is dominated by some field or particle that has negative pressure such that the equation of state: There is a non-zero cosmological constant, . The Friedmann equations are incorrect since they contain oversimplifications in order to make the general relativistic field equations easier to