A hot topic in cosmology is to test gravity on scales well beyond our Solar system. 2015 marks the centenary of Einstein’s publication of his General theory of Relativity (GR), which is still our standard gravity theory. Although GR has been tested rigorously in the Solar system, its application in cosmology is still largely an extrapolation. Previous cosmological observations did not have the precision to test it accurately, but the situation is changing quickly in light of the future galaxy and cluster surveys such as Euclid, LSST, DESI and eROSITA, all of which aim to test GR as a primary science objective. Over the next decade, these observations will determine key cosmological parameters with percent-level precision, and bring the cosmological tests of GR to a similar precision for the first time. They will also address another critical question in modern cosmology – whether the mysterious accelerated expansion of our Universe is due to some unknown exotic matter (dark energy) or a different behaviour of gravity on cosmological scales.
To fully exploit those billion-dollar surveys and to achieve their scientific potential of testing gravity, it is crucial to be able to accurately predict the observable signatures of non-standard gravity theories. This is a numerically intensive problem, which depends critically on powerful supercomputing resources such as DiRAC-2. Indeed, DiRAC has enabled us to make significant progresses over the past few years [1-11]. These efforts have led to developments of state-of-the-art algorithms and simulation codes such as the first ever parallelised N-body code for such theories, ECOSMOG [1-3], as well as a recent code  implementing a novel algorithm to trace light rays across cosmological simulations on the fly. These codes have been used widely in studies of this field, and ruled out popular non-standard models such as Galileon gravity . More recently, tests on DiRAC led an improvement of the performance of ECOSMOG by over 10 times for some theories , making it possible to study such theories by large and high-resolution simulations in the future.
The numerical studies can also have implications to other fields. For example, the Galileon model features nonlinear differential equations similar to the famous Monge-Ampere equation in the optimal transportation problem, and its study has led to a new stable algorithm to solve this type of equation. These previous studies have fully equipped us [8-10] with efficient tools to make accurate predictions for a number of cosmological observables, including weak gravitational lensing, redshift space distortions and clusters of galaxies, for which we expect precise observational data in the next decade. They have prepared us for accurate cosmological tests of gravity and will help to shed light on the understanding of the origin of the accelerated expansion of our Universe. More exciting progresses are expected for the next few years.
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