The early universe consists of a hot and dense photon-baryon plasma. Small density fluctuations in the plasma give rise to acoustic sound waves. These sound waves are driven by radiation pressure and propagate at a relativistic speed. About 400,000 years after the Big Bang, the universe is cool enough for free electrons to be captured by protons to form neutral hydrogen atoms. These newly-formed hydrogen atoms do not interact strongly with photons, and, as a result, photons decouple from the matter. No longer supported by radiation pressure, the baryon sound waves halt, producing density bumps, often called the baryon acoustic oscillations (BAOs), at about $100 h^{-1}Mpc$ detectable in the anisotropy of the cosmic microwave background (CMB) and in the distribution of galaxies.
Evolution of the density profile due to acoustic sound waves in the early universe. Source.
Because BAOs create an excess of galaxies at about $100 h^{-1}Mpc$, they can be detected by studying at the large-scale clustering of galaxies. To do this, physicists often use the spatial two-point correlation function (TPCF). The TPCF is a mathematical tool to contrast between the observed distribution of galaxies and the distribution in which all galaxies are uniformly distributed over the observed volume (referred to as the random distribution). It describes the excess probability (observed over random) of finding two galaxies separated by some separation variables (e.g. distance, angle). With this, BAOs should create a small bump in the spatial TPCF at about 150 Mpc.
BAOs create a bump in the spatial TPCF at the $100h^{-1}Mpc$. Source.
KITCAT, short for the Kd-tree Implementation for Two-point Correlation AlgoriThm, is a simple and fast tool to compute the 1-D and 2-D spatial TPCF of galaxies. By assuming the random distribution can be separated into angular variables (declination and right ascension) and redshift, KITCAT uses convolution of probability distributions to accelerate the computation of the TPCF. Thanks to this, KITCAT also allows for a fast and flexible scan over the cosmological parameter space.
For more information, refer to this paper on which KITCAT is based.
