One big question in the physics of large-scale structures is how we can trace back the evolution of cosmic structures and reconstruct the initial density field. The universe we observe today is dotted with galaxy clusters separated by vast voids, in sharp contrast to its initial state, which was nearly uniform with only minor density fluctuations. The evolution from this early uniformity to today’s complex structure of galaxies is a profound transformation, with many intermediate processes still unexplained. This talk focuses on this transformation, aiming to reconstruct both the initial density and the displacement fields of galaxies observed in spectroscopic surveys. I will discuss new reconstruction algorithms that depend weakly, if at all, on a cosmological model. These algorithms have paved the way for new astrophysical achievements in several directions, such as: Baryon Acoustic Oscillations (BAO) analysis, morphological analysis of proto-halos, and kinematic Sunyaev-Zel’dovich (kSZ) effect.
