During my thesis, I carried out three distinct projects. These projects are independent from each other and investigate various topics of modern Cosmology. A common thread, should one be found, would be the definition of physical observables. This would allow us to test the predictions of General Relativity and to confront it to the so-called Modified Gravity models, although my thesis does not consider such models per se. The standard model of Cosmology describes a homogeneous and isotropic expanding Universe: The FRLW universe. The standard model of Cosmology predicts a pro-portional relationship between the distance to a nearby light source and its redshift. This theoretical prediction is confirmed by observational results. Moreover, the FRLW model also describes the existence of the Cosmological Microwave Background (CMB): A set of photons filling the whole Universe, whose energy distribution follows a black body law.. This theoretical prediction is also observed experimentally and provides a strong proof of the validity of the model.

The first project deals with the invariance of Galaxy Number Counts under conformal transformation. I first present the concept of conformal frames and the associated physical interpretation. With this in mind, I argue that the physical observables should not depend on the chosen frame. Finally, I focus on one observable in particular: The Galaxy Number Counts. As the name suggests, this observable quantifies the angular fluctuations of the number of observed galaxies. I show explicitly that the Galaxy Number Counts is frame-independent, which supports the hypothesis previously stated.

The second project investigates the lensing effect which describes how a mass (or energy) distribution deflects light rays and distorts the images of observed galaxies. I first present the mathematical tools used to quantify lensing, with a focus on cosmic shear. I explain how it can, under certain conditions, induce a rotation of the principal axes of galaxy images. I use this result to build an estimator of the cosmic shear correlation functions. I finally argue that, if the number of galaxies is large enough, the signal-to-noise ratio can be significantly enhanced, which makes this method a competitive one.

In the third project, I study a Schwarzschild Black Hole in a modified effective theory of gravity. In such a theory, new terms are added to the Einstein-Hilbert action in a systematic but agnostic way, i.e. without taking the origin of these terms into consideration. Then, I compute the Schwarzschild Black Hole metric in this theory, perturbatively and at linear order. I then focus on the gravitational waves produced by such a Black Hole. Finally, I compute the correction to their propagation speed and show that this speed can differ from unity, and I determine the corrections to the Quasinormal Modes in this theory.