Description
This talk is dedicated to the modeling and constraint simulations of the distant Universe.
Introducing high redshift observations ($2.5>z>2$) galaxy and Lyman-$\alpha$ forest absorption observations, I will present the reconstruction of the dark matter density field and infer the initial fluctuations compatible with these structures.
Starting from here, I will show the results of our constraint cosmological simulations of these structures until today and the evolution of the most massive (photo-)clusters in this volume. The outcome of this work is especially interesting to understand galaxy formations and its interplay with the intergalactic medium.
Finally I will discuss the link of galaxy redshift and Lyman-$\alpha$ observables and provide a joint interpretation for these reconstructions.
