Analysis of simulated galaxy catalogues at very large scales with relativistic effects.

Redshift space distortions alter the observed distribution of galaxies. These effects are caused by the inhomogeneous distribution of matter in the Universe that sources the galaxies' peculiar velocity and the underlying gravitational potential. Both of these phenomena perturb the path of the upcoming photons emitted by distant sources, changing the measured redshift and angular positions. The distortions caused by this mapping from real to redshift space can be observed in the galaxy power spectrum and higher-order statistics. Two main contributions to the shifts can be recognized: the velocity shifts, due to the peculiar velocities of the galaxies and the observer, and terms depending on the gravitational potential, which include weak lensing, Shapiro time delay, Sach-Wolfe effect and integrated Sach-Wolfe effect. Moreover, the evolution of the tracer's selection function can produce additional distortions, due to the magnification and evolution biases. In general, the non-velocity terms of the shifts are subdominant and have not been observed at the scales that have been probed in surveys up till now, but it is still unclear if the new generation of galaxy surveys (Euclid, DESI), which will look up to z~2, will be able to detect these effects at the largest scales ever probed. The LIGER code, from an N-body simulation, builds light cones of a given tracer in redshift space, applying all the shifts above mentioned. This allows us to compute directly statistics like the power spectrum without using any analytical models. The code can then be used to forecast the performance of upcoming surveys and to assess the importance of relativistic effects. Up until now LIGER has been used in a "field" configuration, i.e. to shift the dark matter particles for low resolution dark matter simulations, instead of shifting directly the tracers. The matter light cones were used to compute various fields in redshift space. Then, via a biasing procedure, a light cone of a tracer could be produced. We refer to this method as "field approach", and it suffers from a series of limitations related to the nature of the biasing procedure and of the input simulation's resolution. For this reason, in my master thesis we write a new implementation of the LIGER code that builds light cones of tracers by mapping them onto redshift space directly, without recurring to the biasing procedure. This approach solves the issues of the field configuration mentioned above, allowing to produce a more realistic galaxy catalogue, that emulates better what a redshift survey would actually observe. We test the code's accuracy at large scales by comparing the power spectrum of the catalogues produced with this new, direct implementation and the field approach. In order to do so, the code is applied on the HugeMDPL simulation, a dark matter only simulation with a 4 Gpc/h box size. We build a set of mock tracers starting from the ROCKSTAR halo catalogues available with the simulation, to which we assign a mock mass-luminosity relation, in order to also study magnification effects. We also build a set of mock catalogues following the field approach, where the required survey functions are directly estimated from the simulation data. We then compare the tracer power spectrum monopole obtained with the two methods. At large scales, the two approaches are shown to be compatible both in real and redshift space, while as we probe smaller scales, we notice that our implementation does not suffer from the same resolution issues as the field approach. Moreover, we make use of the observer's velocity signature on the power spectrum to show that the code correctly captures the evolution and magnification biases.