Weak field general relativistic N-body simulations for cosmic large scale structure

I present a numerical framework which, for the first time, allows one to abandon the Newtonian concept of absolute space and time and do a simulation of cosmic structure formation in a truly dynamical spacetime. In order to avoid the complexity of full general relativity, the framework employs a weak field approximation which is suitable for cosmology, even in the deeply non-linear regime. Since the description is fully relativistic to begin with, any observables which depend on relativistic effects (like lensing or redshift) can be constructed in a transparent way. Moreover, the scheme naturally allows for completely general sources of stress-energy, and can therefore be useful for the investigation of possible alternatives to the standard dark components of the Universe.