  Poincar\'e invariance is a well-tested symmetry of nature and sits at the
core of our description of relativistic particles and gravity. At the same
time, in most systems Poincar\'e invariance is not a symmetry of the ground
state and is hence broken spontaneously. This phenomenon is ubiquitous in
cosmology where Lorentz boosts are spontaneously broken by the existence of a
preferred reference frame in which the universe is homogeneous and isotropic.
This motivates us to study scattering amplitudes without requiring invariance
of the interactions under Lorentz boosts. In particular, using on-shell methods
and assuming massless, relativistic and luminal particles of any spin, we show
that the allowed interactions around Minkowski spacetime are severely
constrained by unitarity and locality in the form of consistent factorization.
The existence of an interacting massless spin-2 particle enforces (analytically
continued) three-particle amplitudes to be Lorentz invariant, even those that
do not involve a graviton, such as cubic scalar couplings. We conjecture this
to be true for all n-particle amplitudes. Also, particles of spin S > 2 cannot
self-interact nor can be minimally coupled to gravity, while particles of spin
S > 1 cannot have electric charge. Given the growing evidence that free
gravitons are well described by massless, luminal relativistic particles, our
results imply that cubic graviton interactions in Minkowski must be those of
general relativity up to a unique Lorentz-invariant higher-derivative
correction of mass dimension 9. Finally, we point out that consistent
factorization for massless particles is highly IR sensitive and therefore our
powerful at-space results do not straightforwardly apply to curved spacetime.
