  We extend the cosmological bootstrap to correlators involving massless
particles with spin. In de Sitter space, these correlators are constrained both
by symmetries and by locality. In particular, the de Sitter isometries become
conformal symmetries on the future boundary of the spacetime, which are
reflected in a set of Ward identities that the boundary correlators must
satisfy. We solve these Ward identities by acting with weight-shifting
operators on scalar seed solutions. Using this weight-shifting approach, we
derive three- and four-point correlators of massless spin-1 and spin-2 fields
with conformally coupled scalars. Four-point functions arising from tree-level
exchange are singular in particular kinematic configurations, and the
coefficients of these singularities satisfy certain factorization properties.
We show that in many cases these factorization limits fix the structure of the
correlators uniquely, without having to solve the conformal Ward identities.
The additional constraint of locality for massless spinning particles manifests
itself as current conservation on the boundary. We find that the four-point
functions only satisfy current conservation if the s, t, and u-channels are
related to each other, leading to nontrivial constraints on the couplings
between the conserved currents and other operators in the theory. For spin-1
currents this implies charge conservation, while for spin-2 currents we recover
the equivalence principle from a purely boundary perspective. For multiple
spin-1 fields, we recover the structure of Yang-Mills theory. Finally, we apply
our methods to slow-roll inflation and derive a few phenomenologically relevant
scalar-tensor three-point functions.
