  We extend the investigation of the structure of the late-time wavefunction of
the universe to a class of toy models of scalars with time-dependent masses and
polynomial couplings, which contains general massive scalars in FRW
cosmologies. We associate a universal integrand to each Feynman diagram
contributing to the wavefunction of the universe. For certain (light) masses,
such an integrand satisfies recursion relations involving differential
operators, connecting states with different masses and having, as a seed, the
massless scalar (which describes a conformally coupled scalar as a special
case). We show that it is a degenerate limit of the canonical form of a
generalisation of the cosmological polytopes describing the wavefunction for
massless scalars. Intriguingly, the flat-space scattering amplitude appears as
a higher codimension face: it is encoding the leading term in the Laurent
expansion as the total energy is taken to zero, with the codimension of the
face providing the order of the total energy pole. The same connection between
the other faces and the Laurent expansion coefficients holds for the other
singularities of the wavefunction of the universe, all of them connectable to
flat-space processes. As the degenerate limit is taken, some of the
singularities of the canonical form of the polytope collapse onto each other
generating higher order poles. Finally, we consider the mass as a perturbative
coupling, showing that the contribution to the wavefunction coming from graphs
with mass two-point couplings can be identified with a degenerate limit of the
canonical form of the cosmological polytope, if the perturbative expansion is
done around the conformally coupled state; or as double degenerate limit of the
canonical form of the extension of the cosmological polytopes introduced in the
present paper, if the perturbative expansion is done around minimally coupled
states.
