The unitarity of time evolution is a vitally important constituent of our descriptions of fundamental interactions via quantum field theory. The implications of unitarity for scattering amplitudes are well understood, for example through the optical theorem and cutting rules. In contrast, the implications for interactions in curved spacetimes are only now beginning to be investigated. Understanding such curved spacetimes is vital to deepening our knowledge of the early universe where, within the leading paradigm, we expect an approximately de Sitter expansion. In this thesis we show that unitarity implies a set of relations among the coefficients of the wavefunction of the universe in such an expanding epoch, which we name the cosmological optical theorem. We also show that this result can equivalently be understood as a single cut rule that relates diagrams at different orders in perturbation theory. The validity of this relationship is explored within the cosmological context, and we present several explicit checks of this relation. Finally, we demonstrate the power of this result by using it to derive the graviton four-point wavefunction coefficient. This requires some additional recent developments in the cosmological bootstrap program exploiting locality and the relationship to flat space amplitudes which are reviewed.