  We argue that a plausible operational definition for an initial state of the
Universe is the initial quantum state of the curvature perturbations generated
during inflation. We provide a parameterization of this state and generalize
the standard in-in formalism to incorporate the structures in this state into
the computation of correlators of the perturbations. Measurements of these
correlators using both the CMB as well as large scale structure probe different
structures in the initial state, as they give rise to bi- and tri-spectra
peaked on different shapes of triangles and quadrilaterals in momentum space.
In essence, the shapes implied by the correlators feed directly into
information about the shape of the initial state and what physics could have
preceded inflation to set this state up.
