Description
The evolution of our Universe is driven by two competitive mechanisms : expansion and gravity. From small homogeneous perturbations, the Universe has turned cold and structured and is now filled with luminous galaxies. Hence, measuring the growth of the large scale structures, through their peculiar velocities, is a key probe to both expansion and gravity and can precisely determine the nature of dark energy and validate General Relativity. Peculiar velocity measurements rely on precise extragalactic distances estimation so that the future of peculiar velocity analyses lies in Type Ia Supernovae observations from ZTF and, then, LSST campaigns. Since peculiar velocities of galaxies are deviations from the Hubble expansion law, they have poor signal to noise ratio and are particularly sensible to usual systematic uncertainties such as calibration errors, selection effects, unknown covariances etc. During this presentation I will show how a precise forward modeling of observations allow us to overcome these caveats and that peculiar velocities analyses can be considered as a powerful cosmological probe. In particular, I will detail how the statistical methods I developed during my thesis can handle extragalactic distance measurements and lead to - e.g. - a velocity field reconstruction of our Local Universe from Type Ia Supernovae, so as constraints on General Relativity.