  In the context of Effective Field Theory, the Hilbert space of states
increases in an expanding universe. Hence, the time evolution cannot be
unitary. The formation of structure is usually studied using effective field
theory techniques. We study the constraints on effective field theory analyses
of early universe models which come from demanding that the factor of the space
of states corresponding to length scales where the primordial fluctuations are
manifest does not suffer from the unitarity problem. For bouncing and emergent
cosmologies, no constraints arise provided that the energy scale of the bounce
or emergent phases is smaller than the ultraviolet (UV) cutoff scale. On the
other hand, in the case of the inflationary scenario, non-trivial upper bounds
on the energy scale of inflation arise.
