| Abstract: The current and upcoming surveys in cosmology will soon deliver an unprecedented amount of precision measurements, truly opening an era of precision cosmology. However, this rapid development in experiments and observations demands substantial advances in theoretical modeling to avoid any systematic errors in our interpretation. The standard theoretical descriptions of galaxy clustering, weak gravitational lensing, and the CMB Boltzmann equations are incomplete and limited to the linear-order perturbation theory, because of two closely related issues: gauge dependence and the observer frame. All theoretical descriptions of cosmological observables should be independent of our coordinate choice, i.e., gauge-invariant. Furthermore, while these observables are measured by the observer, there is no specification of the observer in the standard model. The observer and its rest frame is indeed necessary to properly connect the cosmological observables with QFT calculations in Minkowski space and to derive their fully nonlinear equations. I will describe my ongoing research program to re-write cosmology in the proper relativistic framework, and I will highlight the impact of the missing physics on cosmological observables. |