School of Physical and Chemical Sciences Te Kura Matū Seminar Series

On the Lagrangian perturbation theory of structure formation in general relativity


Yong-Zhuang Li, PhD candidate under supervision of David Wiltshire and Chris Gordon


School of Physical and Chemical Sciences, University of Canterbury

Time & Place

Mon, 12 Nov 2018 11:00:00 NZDT in Room 119 - Engineeing

All are welcome


It is widely accepted that the large scale structures of the present Universe are the result of gravitational amplification of small primordial fluctuations. Over many decades of research in cosmology, large scale structure formation has been modeled on the basis of a perturbative approach, which makes use of the instability of the standard cosmologies of Friedmann-Lemaitre type against perturbations of the density and velocity fields. The perturbations are evaluated as a function of Eulerian coordinates in this approach and rely on physical densities being small. Beyond the linear regime the N-body simulation has been employed to investigate the structure formation.

An alternative approach has also been developed in last few decades, which is known as the Lagrangian perturbation theory (LPT)1. In contrast to the Eulerian perturbation theory, only the deviations of the particle trajectories from the homogeneous Hubble flow are treated perturbatively. The field of trajectories is the only dynamical variable in the Lagrangian picture. This gives the LPT the advantage of also applying in the nonlinear regime. 

To develop a fully relativistic description of structure formation in the realistic Universe within the context of LPT, the Newtonian Lagrangian perturbation theory for two fluids in relative motion has been investigated as a first step.  A relativistic Lagrangian perturbation theory for a single irrotational fluid is then developed as a further forward2.

1: T. Buchert, "Lagrangian perturbation theory: a key-model for large-scale structure", Astron. Astrophys., 267: L51-L54 (1993).
2: Yong-zhuang Li, Pierre Mourier, Thomas Buchert, David L. Wiltshire, “Lagrangian theory of structure formation in relativistic cosmology. V. Irrotational fluids”, Phys. Rev. D 98: 043507 (2018).