Cosmological observations are advancing quickly, extending to larger scales and higher redshifts, and becoming ever more precise. In order to understand the implications of this incoming data, our theoretical modelling must improve at the same pace.
The next generation of large scale structure measurements, such as the Euclid satellite, the Square Kilometre Array (SKA) and the Large Synoptic Survey Telescope (LSST), will go to very high redshifts and map very large fractions of the sky. These will probe scales that were beyond the matter-radiation-equality scale and even causally disconnected at the time their light was emitted, meaning that relativistic effects and ambiguities in defining observables can be important. Failing to properly account for such effects could lead to biases in our inferences about the Universe.
Theoretical treatments of cosmological observations have always been approximate. Calculations of cosmic microwave background (CMB) anisotropies are fully relativistic, but are usually limited to the linear approximation. ICG researchers developed a fully second order Einstein-Boltzmann code, Second Order Non-Gaussianity (SONG).
On the other hand, large-scale structure observations are intrinsically non-linear; the theoretical predictions are usually determined using N-body simulations that assume Newtonian gravity. While this is an excellent approximation on small scales, it misses essential relativistic effects that become important on scales of order the horizon size. In addition, usual treatments often ignore general relativistic effects on the observations that can arise along the photon line-of-sight.
Relativistic Interpretation of Newtonian Simulations
In recent papers we have developed the Newtonian motion gauge framework, which constructs a relativistic space-time within which Newtonian N-body simulations can be interpreted. It uses the gauge freedom of general relativity to construct a spatial coordinate threading of space-time in which the relativistic particle trajectories coincide with the Newtonian trajectories computed in a conventional N-body. This introduces a convenient split between the non-linear computation of particle trajectories in the Newtonian theory and the perturbative evolution of the metric potentials in the relativistic theory. These problems can be solved independently, with the Newtonian motion gauge providing a consistent framework to combine them when generating initial conditions and when interpreting the output.
Relativistic galaxy bispectrum
The cosmological information from power spectrum measurements is limited. Observations are already turning to the galaxy bispectrum, and this is a natural place to look for nonlinear corrections from general relativity. ICG researchers made second-order calculations of the observed galaxy number density and the bispectrum from the local effects, showing that the relativistic galaxy bispectrum can be detected in future surveys such as Euclid.
ICG faculty researching Relativisitc Cosmology include: