Research

There is no question that the widely-used cosmological framework of Newtonian gravity on small scales + perturbed FLRW on large scales provides only an approximate (albeit surprisingly accurate) description of our Universe.
Many people have worked on improving this description with general-relativistic corrections, mostly in the form of post-Newtonian and post-Friedmannian methods, and/or higher-order perturbation theory. Even still, most of these methods are honest about what they are: approximations. These approximations (i.e. perturbation theory or Newtonian gravity) are usually considered because they are easier to work with than the full problem.
With the advancements in Numerical Relativity (NR) over the past decade or so, this is no longer necessarily the case.
As the precision of our data improves, tensions between cosmological observations and LCDM are growing. Some of these tensions can be relieved when considering inhomogeneous cosmological (toy) models. However, the simplistic nature of many of these models make drawing conclusions for our own Universe difficult.
Considering the truly inhomogeneous nature of our Universe in full is impossible analytically. NR provides us with a framework to study general-relativistic effects in cosmology without simplifying assumptions for gravity or geometry, whilst still capturing the complex structure of matter that we observe.
The simulation snapshot at the top of the page is one of the first realistic cosmological simulations performed with NR. For more details see my papers here and here.

Software

We use the free, open-source Einstein Toolkit (based on the Cactus infrastructure), along with our cosmological initial-condition module FLRWSolver.
A working (but currently limited) version of FLRWSolver is available, see here for instructions on downloading and compiling, and a brief tutorial on running a simple simulation here.
Feel free to contact me with any issues getting started with the code.
Please remember to cite this paper if you use FLRWSolver in any presentation, publication, or communication.

To extract interesting things from Cactus in post-processing we use my analysis code mescaline (which will be made public in the future).

Data

If you don't want to run a simulation yourself, a bunch of my data is freely available for download here.
Feel free to contact me with any questions about the data.