Conformal anomalies and gravitational waves

We argue that the presence of conformal anomalies in gravitational theories can lead to observable modifications to Einstein's equations via the induced anomalous effective actions, whose non-localities can overwhelm the smallness of the Planck scale. The fact that no such effects have been seen in recent cosmological or gravitational wave observations therefore imposes strong restrictions on the field content of possible extensions of Einstein's theory: all viable theories should have vanishing conformal anomalies. We then show that a complete cancellation of conformal anomalies in D=4 for both the C2 invariant and the Euler (Gauss-Bonnet) invariant E4 can only be achieved for N-extended supergravity multiplets with N⩾5, as well as for M theory compactified to four dimensions. Although there remain open questions, in particular concerning the true significance of conformal anomalies in non-conformal theories, as well as their possible gauge dependence for spin s⩾32, these cancellations suggest a hidden conformal structure of unknown type in these theories.