Signs of Analyticity in Single-Field Inflation
  The analyticity of response functions and scattering amplitudes implies
powerful relations between low-energy observables and the underlying
short-distance dynamics. These 'IR/UV' relations are rooted in basic physical
principles, such as causality and unitarity. In this paper, we seek similar
connections in inflation, relating cosmological observations to the physics
responsible for the accelerated expansion. We assume that the inflationary
theory is Lorentz invariant at short distances, but allow for non-relativistic
interactions and a non-trivial speed of propagation at low energies. Focusing
on forward scattering, we derive a 'sum rule' which equates a combination of
low-energy parameters to an integral which is sensitive to the high-energy
behavior of the theory. While for relativistic amplitudes unitarity is
sufficient to prove positivity of the sum rule, this is not guaranteed in the
non-relativistic case. We discuss the conditions under which positivity still
applies, and show that they are satisfied by all known UV completions of
single-field inflation. In that case, we obtain a consistency condition for
primordial non-Gaussianity, which constrains the size and the sign of the
equilateral four-point function in terms of the amplitude of the three-point
function. The resulting bound rules out about half of the parameter space that
is still allowed by current observations. Finding a violation of our
consistency condition would point towards less conventional theories of
inflation, or violations of basic physical principles.
