
A technique to partially undo late-time gravitational distortions in galaxy clustering data.Reconstruction is a data-processing technique used in cosmology to partially undo the late-time gravitational distortions that obscure the primordial patterns in galaxy clustering. In the early universe, tiny density fluctuations left an imprint on the distribution of matter, a pattern known as baryon acoustic oscillations (BAO). As the universe evolved, the gravitational pull of large-scale structures — dark matter halos, galaxy clusters, and filaments — shifted galaxies from their original positions, smearing out this signal. Reconstruction aims to reverse these shifts statistically, sharpening the BAO feature and improving measurements of cosmic distances.
The technique was introduced in the early 2000s by Daniel Eisenstein and colleagues, who proposed it as a way to enhance the BAO signal in galaxy surveys. It has since become a standard tool in cosmological analyses.
The method works by estimating the displacement field of galaxies using the observed galaxy distribution itself. From the density field, one computes the gravitational potential and then moves galaxies back along the inferred trajectories, effectively 'undoing' the bulk flows caused by large-scale structure. This is done iteratively or with a single step, depending on the algorithm. The result is a reconstructed density field that more closely resembles the initial conditions, with the BAO peak in the correlation function becoming sharper and more detectable.
Reconstruction is routinely applied in large galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) and the Euclid mission, to sharpen BAO measurements and constrain dark energy parameters.
Reconstruction can improve the precision of BAO distance measurements by roughly a factor of two, effectively doubling the survey's statistical power without observing more galaxies.








