  In this thesis, I present three projects I carried out during m PhD. In the
first project, I introduce Conformal Transformations and the Galaxy Number
County. I explicitly show that the Galaxy Number Counts is invariant under
Conformal Transformations, which makes it a good physical observable. In the
second project, I study how weak lensing, and in particular cosmic shear,
affects the shape of the galaxy images. I show that, if the light polarisation
is also measured, the rotation of the main axes of the elliptical galaxy shape
becomes a cosmological observable. I show how this can be used to estimate
cosmic shear and its correlation functions. In the third project, I define a
higher order (Riemann-squared and -cubed) Lagrangian Effective Theory of
Gravity. I compute the linear correction to the speed and the quasinormal
frequencies of the gravitational waves in this theory around a
Schwarzschild-like background.
