Einstein's Universe: Cosmological Structure Formation in Numerical Relativity*

The era of precision cosmology is well underway. Additional constraining power of upcoming large datasets will not only allow us to narrow the error bars on well-established cosmological parameters, but to extend our modelling beyond current simplifying assumptions. General relativity is one of the most important ingredients in our standard cosmological model. However, throughout cosmology we adopt a variety of approximations within general relativity, the validity of which must be constantly and rigorously tested as the precision of our data improves. 

A key assumption in modern cosmology is the validity of the exactly homogeneous and isotropic Friedmann–Lemaitre–Robertson–Walker (FLRW) models in describing the large-scale geometry of the Universe. The use of the FLRW models is often justified by the statistical homogeneity of the galaxy distribution on large scales and the observed isotropy of the cosmic microwave background radiation. Neither of these conditions, together or alone, guarantee that the geometry of the Universe is close to FLRW. Applying numerical relativity to simulations of large-scale structure formation allows us to remove the simplifying assumptions for gravity and geometry which are commonly adopted in cosmology. While approximations have been vital in advancing cosmology to the level we are at today, all approximations will break down eventually. Whether this breakdown is only reached once surveys surpass percent-level precision, or if we are already seeing it in the form of the growing number of “tensions” between model predictions and observation, is yet to be determined. Numerical relativity offers the ideal framework within which to accurately determine the validity of our approximations as well as study nonlinear general-relativistic effects. 

I will present a brief history of the application of numerical relativity to cosmology before presenting my own work investigating synthetic cosmological observables computed from first principles in general relativity.