In flat space, four point scattering amplitudes at weak coupling can be fully determined from Lorentz symmetry, unitarity and causality. The resulting scattering amplitude depends on model details only through coupling constants and the particle content of the theory. I will show how the analogous story works in the case of inflationary fluctuations. We found explicit expressions for inflationary three and four-point functions, whose shapes depend on the field content of the theory, and do not depend on the specific inflationary model, as long as the fluctuations minimally break de Sitter symmetry. This ``cosmological bootstrap” is a first step towards classifying all possible shapes of primordial non-gaussianity, which can be searched for in experimental data.