Tensor squeezed limits and the Higuchi bound

Abstract

We point out that tensor consistency relations-i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum-are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: De Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor consistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) Graviton exchange contribution to the scalar four-point function; (b) Quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.

Non-Gaussianity as a particle detector

“…This signal may be observable in the BT T correlator of CMB anisotropies [58]. 22 A deviation from the leading term of the consistency relation due to spinning particles can arise in a number of ways: first, the unitarity bound can be evaded if the de Sitter isometries are not fully respected in the quadratic action of the spinning field [60,61]. Another possibility involves partially massless fields with spin greater than two, since the late-time behavior of these fields does not obey the same restrictions as for the massive case.…”

Large gauge transformation, soft theorem, and Infrared divergence in inflationary spacetime

“…[14,70]). The quantum state | Ψ changes due to the single insertion of the soft graviton, i.e., 9) because the wave function is not completely flat in the direction of the soft graviton γ ij k L with k L = 0 in contrast to the homogeneous mode, whose wave function is completely flat, satisfying eq.…”

Spatial curvature at the sound horizon

“…The most famous soft theorem has been derived by Maldacena in [6] and fixes the squeezed bispectrum in terms of the power spectrum and it applies to all attractor, singlefield models of inflation [7]. This first result has been extended to higher n-point functions for primordial scalar, tensor and vector perturbations [8,9,10,11,12,13,14,15,16,17,18,19]. Soft theorems are conveniently interpreted as the consequence of residual, non-linearly realized symmetries associated with adiabatic modes [20,9,21,18,22], namely physical perturbations that are indistinguishable from a change of coordinates in the neighborhood of a point in spacetime.…”

“…We also neglect slow-roll suppressed terms in our estimation of the signal-to-noise ratio. 17 Notice that we use the flat universe prediction for the transfer functions used to compute C l as opposed to the transfer functions in a curved universe. The difference is only of order ΩK , much smaller than the ΩK /c 2 s effect that we are after here.…”