Cosmological simulations of large scale structure and general relativity

The current standard model of cosmology, LCDM, assumes Cold Dark Matter and a cosmological
constant Lambda as Dark Energy, and is based on three main ingredients:
1) the Universe is isotropic and homogeneous on the largest scales and thus well described the
Friedmann-Lemaitre-Robertson-Walker (FLRW) metric;
2) large-scale structure can be modelled by perturbative methods, linear and non-linear;
3) fully nonlinear structure formation can be described by Newtonian N-body simulations.
This project will address the question of how good this last assumption is. The modern theory of
gravity is, after all, General Relativity. With state-of-the-art cosmological observations reaching a
precision of 1% or better and even more improvement expected in the near future, it is extremely
timely to investigate how accurate the current theoretical predictions are.
There are now publicly available Newtonian N-body codes, as well as N-body codes that include
corrections from General Relativity, that can be used to model large-scale structure in cosmology.
However, it is far from clear that these codes including some relativistic corrections capture all the
important effects. On the other hand, we recently successfully applied numerical relativity codes (i.e.
codes that are fully relativistic) in cosmology for the first time, albeit in a very simplified setting and
using a fluid description of matter, rather than the particle description of N-body codes. This PhD
project will build on these first pioneering works to further develop a fully relativistic approach to the
study of large-scale structure. One important goal is to establish how accurate Newtonian and "GRcorrected" codes are; another is to test various general-relativist approximations used to model
structure formation in the mildly-non-linear regime; these issues can be addressed by using existing
numerical relativity codes as benchmark. Another open problem to address is that of accurately
implementing relativistic initial conditions derived from perturbation theory into the nonlinear evolution.
There is a number of physical questions that need investigation in full GR, from the collapse of the first
cosmological objects to the formation of large voids, to how the formation of nonlinear structures
affects light propagation in cosmology, ultimately affecting observations.