Self-dual cosmology

We construct cosmological spacetimes with a self-dual Weyl tensor whose dynamics are described by conformally coupled scalars with only cubic self-interactions. Similar to the previously discovered cases in flat and (Anti) de Sitter backgrounds, the interactions are characterized by a bracket that encodes a kinematic algebra. We discuss how the color-kinematics duality and double copy are realized in these cosmological backgrounds. If we further impose that the Ricci scalar is that of an FLRW spacetime, we find two new self-dual metrics corresponding to radiation-dominated and coasting (non-accelerating) FLRW backgrounds. Relaxing this requirement, we find an infinite family of solutions given by three different conformal classes of cosmological self-dual metrics. These solutions approximate those of FLRW as long as we impose a simple additional constraint on the scalar theory.