Sample optimization for the detection of relativistic effects with galaxy power spectrum measurements.

In measurements of cosmological interest, the density contrast of galaxies is used to map the matter distribution in the Universe. The relation between the density contrast of matter and that of galaxies has some corrections, amongst which a purely imaginary term due to general relativity. Such an effect, which brings additional contributions to the power spectrum of galaxies, is sub-dominant compared to the standard Newtonian contributions. This work focuses on optimizing the sample to be studied to measure such a relativistic effect in the power spectrum of galaxies. The relativistic effect depends mainly on the characteristics of the investigated sample ($e.g.$, luminosity function). In fact, it is the large-scale part of the power spectrum that is mainly affected by this correction. I will present forecasts for the detection of the relativistic effect for some future galaxy surveys by measurements of the auto- and cross-correlation power spectra of several galaxy samples. Cross-correlation measurements appear to be more promising than auto-correlation measurements, as they allow the studied effect to be detected even at smaller scales.