Dan Thomas tells us about recent work first creating a framework for describing modified gravity in a model independent way on non-linear scales and then running N-body simulations in that framework.
The framework involves finding a correspondence between large scale linear theory where everything is under control and small scale non-linear post-Newtonian dynamics. After a lot of care and rigour it boils down to a modified Poisson equation – on both large and small scales (in a particular gauge).
The full generality of the modification to the Poisson equation allows, essentially, for a time and space dependent value for Newton’s constant. For most modified gravity models, the first level of deviation from general relativity can be parameterised in this way (and we know that the deviations from general relativity are small because so far we haven’t found any!!)
The cosmological simulations are then done by having Newton’s constant just vary over time (i.e. it is constant in space). This allows them to actually do some simulations, but in future work they will go beyond this particular simplification.
They then compare the simulation results to semi-analytic models like Halofit and ReACT. Halofit is explicitly just applicable to ΛCDM model but does surprisingly well. ReACT however still does much better at fitting e.g. the matter power spectrum and model Euclid lensing observables.
Future work will examine more closely why ReACT fits so well and aim to improve the fit even better so that e.g. Euclid and/or the Vera C. Rubin Observatory (LSST) will be able to use this method to constrain modified gravity without needing to run a new simulation for every step of a Monte Carlo parameter fit.
Theory framework paper: https://arxiv.org/abs/2004.13051
Simulation paper: https://arxiv.org/abs/2103.05051
Cosmology Talks 