  A non-singular cosmological bounce in the Einstein frame can only take place
if the Null Energy Condition (NEC) is violated. We explore situations where a
single scalar field drives the NEC violation and derive the constraints imposed
by demanding tree level unitarity on a cosmological background. We then focus
on the explicit constraints that arise in P(X) theories and show that
constraints from perturbative unitarity make it impossible for the NEC
violation to occur within the region of validity of the effective field theory
without also involving irrelevant operators that arise at a higher scale that
would enter from integrating out more massive degrees of freedom. Within the
context of P(X) theories we show that including such operators allows for a
bounce that does not manifestly violate tree level unitarity, but at the price
of either imposing a shift symmetry or involving technically unnatural small
operator coefficients within the low-energy effective field theory.
