Lagrangian theory of gravitational instability of Friedman-Lematre cosmologies - a generic third-order model for non-linear clustering

The Lagrangian perturbation theory of Friedman–Lemaître cosmologies, which was investigated and solved up to the second order in earlier papers, is evaluated up to the third order. Based on this, a model for non-linear clustering applicable to the modelling of large-scale structure in the Universe for generic initial conditions is formulated. A truncated model is proposed which represents the ‘main body’ of the perturbation sequence in the early non-linear regime by neglecting all gravitational sources that describe interaction of the perturbations. I also, however, give the irrotational solutions generated by the interaction terms to the third order, which induce vorticity in Lagrangian space. The consequences and applicability of the solutions are put into perspective. In particular, the model presented enables the study of pre-virialization effects in gravitational clustering and the onset of non-dissipative gravitational turbulence within the cluster environment.