The advent of large spectroscopic surveys of galaxies in the early 1980s has shown us that galaxies assemble in large scale structures.
Recently, cosmic voids have received more attention through the availability wide and deep galaxy surveys. Voids have a simple phase space structure and thus are easier to model than cluster of galaxies.
I will present two important applications of the precise analysis of voids in the context of constraining the equation of state of dark energy. First I will discuss how they could be used to have a much better determination of the expansion factor than using traditional methods, like Baryonic Acoustic Oscillations. Second, I will show that voids is maybe the only large-scale structure for which the dynamics can be finely modelled, notably through the use of the Monge-Ampere-Kantorovitch orbit reconstruction method.
For the two above cases, I will present how we can mathematically define cosmic voids, the methods that have been developed to find them and some results based on N-body simulations for constraining the Dark Energy equation of state.