  Unitarity of time evolution is one of the basic principles constraining
physical processes. Its consequences in the perturbative Bunch-Davies
wavefunction in cosmology have been formulated in terms of the cosmological
optical theorem. In this paper, we re-analyse perturbative unitarity for the
Bunch-Davies wavefunction, focusing on: 1) the role of the
$i\epsilon$-prescription and its compatibility with the requirement of
unitarity; 2) the origin of the different "cutting rules"; 3) the emergence of
the flat-space optical theorem from the cosmological one. We take the
combinatorial point of view of the cosmological polytopes, which provide a
first-principle description for a large class of scalar graphs contributing to
the wavefunctional. The requirement of the positivity of the geometry together
with the preservation of its orientation determine the
$i\epsilon$-prescription. In kinematic space it translates into giving a small
negative imaginary part to all the energies, making the wavefunction
coefficients well-defined for any value of their real part along the real axis.
Unitarity is instead encoded into a non-convex part of the cosmological
polytope, which we name optical polytope. The cosmological optical theorem
emerges as the equivalence between a specific polytope subdivision of the
optical polytope and its triangulations, each of which provides different
cutting rules. The flat-space optical theorem instead emerges from the
non-convexity of the optical polytope. On the more mathematical side, we
provide two definitions of this non-convex geometry, none of them based on the
idea of the non-convex geometry as a union of convex ones.
