Irreversibility of quantum field theory in de Sitter: the C, F and A theorems

We prove the C, F and A irreversibility theorems in de Sitter spacetime for quantum field theories that are obtained as renormalization group flows from ultraviolet conformal fixed points. The proof is based on strong subadditivity of the entanglement entropy, de Sitter invariance, and the Markov property of conformal field theory.