  Massless spinning correlators in cosmology are extremely complicated. In
contrast, the scattering amplitudes of massless particles with spin are very
simple. We propose that the reason for the unreasonable complexity of these
correlators lies in the use of inconvenient kinematic variables. For example,
in de Sitter space, consistency with unitarity and the background isometries
imply that the correlators must be conformally covariant and also conserved.
However, the commonly used kinematic variables for correlators do not make all
of these properties manifest. In this paper, we introduce twistor space as a
powerful way to satisfy all kinematic constraints. We show that conformal
correlators of conserved currents can be written as twistor integrals, where
the conservation condition translates into holomorphicity of the integrand. The
functional form of the twistor-space correlators is very simple and easily
bootstrapped. For the case of three-point functions, we verify explicitly that
this reproduces known results in embedding space. We also perform a
half-Fourier transform of the twistor-space correlators to obtain their
counterparts in momentum space. We conclude that twistors provide a promising
new avenue to study conformal correlation functions that exposes their hidden
simplicity.
