Description
One fundamental 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 a new reconstruction algorithm based on optimal transport theory that depends weakly, if at all, on a cosmological model. This theory deals with moving objects from one place to another while conserving mass and minimizing effort. In a cosmological context, it involves mapping the observed galaxy distribution back to its initial uniform state, minimizing the displacement of galaxies. In this framework, we are able to reconstruct the position and shape of biased tracers in Lagrangian space, in addition to the displacement field, which can be used to reconstruct the initial overdensity fluctuation field
