Cosmology poses unique theoretical challenges at the interface between Quantum Field Theory (QFT) and General Relativity (GR). The time dependence of cosmological spacetimes, upon which quantum fields propagate, spontaneously breaks time translation and Lorentz boost invariance. Thus the usual tools of particle physics, which assume full Lorentz invariance, need to be adapted to the study of cosmological theories. Using Effective Field Theory (EFT) techniques, universal predictions can be made about the dynamics of fluctuations around cosmological backgrounds (e.g. the EFT of Inflation). However, exploring the structure of these cosmological EFTs, such as their regime of validity, still requires tools adapted to their particular set of symmetries. In this thesis we focus on the sub-horizon regime of cosmological EFTs, where the effect of the background curvature can be neglected. This leads us to study flat space EFTs around time-dependent vacua. We explore the landscape of such theories whose structure is fixed by additional symmetries. We show how to modify EFT power counting rules and perturbative unitarity methods when Lorentz boosts are spontaneously broken. This allows us to determine the region of parameter space for which cosmological EFTs are weaklycoupled on sub-horizon scales. Finally we provide a new way to derive positivity bounds and constrain which parts of this parameter space admit unitary and causal UV completions. Comparing with observational constraints on primordial non-Gaussianities, they give us new ways to unravel the physics of inflation.