CFTs Blueshift Tensor Fluctuations Universally
  The strong constraints of conformal symmetry cause any nearly-conformal
sector to blueshift tensor fluctuations in cosmology. Hidden sectors with
approximate conformal symmetry, which may be quite large, are a well-motivated
extension of physics beyond the Standard Models of particle physics and
cosmology. They can therefore lead to a detectable shift in the tensor tilt for
next-generation CMB and gravitational wave experiments. We compute the
leading-order contribution to the in-in graviton two-point function from
virtual loops in such sectors to demonstrate this universal effect. In units
where a single conformally-coupled scalar is 1, limits from Stage-IV CMB
experiments could bound the size of this extra sector to be smaller than about
10^15. This would be sufficient to rule out N-Naturalness as a complete
resolution of the hierarchy problem.
