  Explorations of the violation of null energy condition (NEC) in cosmology
could enrich our understanding of the very early universe and the related
gravity theories. Although a fully stable NEC violation can be realized in the
``beyond Horndeski'' theory, it remains an open question whether a violation of
the NEC is allowed by some fundamental properties of UV-complete theories or
the consistency requirements of effective field theory (EFT). We investigate
the tree-level perturbative unitarity for stable NEC violations in the contexts
of both Galileon and ``beyond Horndeski'' genesis cosmology, in which the
universe is asymptotically Minkowskian in the past. We find that the
constraints of perturbative unitarity imply that we may need some unknown new
physics below the cut-off scale of the EFT other than that represented by the
``beyond Horndeski'' operators.
