A modified least action principle allowing mass concentrations for the early universe reconstruction problem

Yann Brenier (1, 2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 IWD - Institut Wolfgang Döblin

We address the early universe reconstruction (EUR) problem (as considered by Frisch and coauthors), and the related Zeldovich approximate model. By substituting the fully nonlinear Monge-Ampere equation for the linear Poisson equation to model gravitation, we introduce a modified mathematical model, for which the Zeldovich approximation becomes exact. The MAG model enjoys a least action principle in which we can input mass concentration effects in a canonical way, based on the theory of gradient flows with convex potentials and somewhat related to the concept of self-dual Lagrangians developped by Ghoussoub. A fully discrete algorithm is introduced for the EUR problem in one space dimension

Domaines: Equations aux dérivées partielles [math.AP]

Yann Brenier. A modified least action principle allowing mass concentrations for the early universe reconstruction problem. 2010. ⟨hal-00488716⟩