Measuring relativistic corrections with a quadratic estimator for the galaxy power spectrum

The analysis of the large-scale structure of the Universe represents one of the most promising research fields in Cosmology in the next years. The continuous rising of the amount of data available from the surveys has brought us in the era of the precision cosmology, that means that our understanding in the Universe can be tested up to a pre- cision level that was before impossible. In the last two decades, many experiments have been developed to this aim, leading to the development and observational confirmation of the concordance model ΛCDM (Lambda Cold Dark Matter), which describes the evolution of the components of the Universe. This model is far from be complete and very big questions still domain our understanding of the Universe, such as the nature of the Dark Matter and dark Energy, so it is crucial to use all the information we have available. In the Large Scale Structure field is well known that the study of the Redshift Space Distortions is one of the most interesting and promising subject, since they allow to test theory up to very large scales. They are due to the peculiar motion of the galaxies that alter the pattern of the galaxy configuration observed in the surveys, so it is crucial to account for them in order to recover a real map of the Universe. Nowadays modern galaxy surveys can observe very large and deep region, almost approaching the Hubble radius, and so can be demonstrated that, together with the Redshift Space Distortions, at this scale also General Relativistic effects such as Sachs-Wolfe effect (standard and integrated), Doppler and gravitational lensing and Shapiro time delay can modify the observed positions of the galaxies in Redshift space. The 3D map of a survey is a com- bination of the Redshift space distortions due to the peculiar velocity and the General relativistic effects. In this thesis we try to understand if these effects can leave an im- print in the Power Spectrum of a galaxy survey, making them distinguishable. In order to do this we use the LIGER code to create galaxy catalogs that contains these effects. We compute the Power Spectrum for these catalogs comparing them and understand- ing if they presents some differences. The different behavior that we are searching is dominant only in the large scale part of the Power Spectrum, where however the effect of the window function of the specific survey is dominant. It tends to flatten the power spectrum at large scale, destroying the information of the redshift space distortions, so the difference between the various Power Spectrum would be impossible to measure. We overlap this issue computing the Power Spectrum of the mock catalogs using the "Quadratic Estimator" code by Oliver Philcox that takes as input a galaxy mock and measure its Power Spectrum without the effects of the window function, making our analysis possible at all scales.