First, I will present a method I developed to treat cosmological perturbations at linear order, called the Effective Field Theory for Dark Energy (EFT of DE). It has the advantage of quantifying deviations from the standard model $\Lambda$CDM in compact and model independent manner. Secondly, I will discuss new theories that I discovered, that extend Horndeski theories, which were thought to be the most general theories to describe a system gravity + scalar that is stable. Indeed, I will argue that the usual conditions that are required for a theory to be stable, namely that its equations of motion are second-order in derivatives, are too restrictive. Then, I will show the work I did on primordial gravitational waves. More precisely, I will explain how the standard predictions for tensor modes coming from inflation are very robust, contrarily to the scalar ones. This implies in particular that measuring the power spectrum from gravitational waves would give a direct access to the energy scale of inflation. Finally, I will end by a description of my studies on consistency relations. These are relations between the n+1 and n correlations functions of the cosmic density fields when one of the fields varies much less than the others. They are interesting since the derivation needs very little information on the rapidly varying fields: only that their initial conditions are Gaussian and that they obey the Equivalence Principle. \\ \\ PhD supervisor: Filippo Vernizzi.