We investigate primordial tensor non-Gaussianity in single field inflation,
during a phase of non-attractor evolution when the spectrum of primordial
tensor modes can be enhanced to a level detectable at interferometer scales.
Making use of a tensor duality we introduced in arXiv:1808.10475, we
analytically compute the full bispectrum of primordial tensor fluctuations
during the non-attractor era. During this epoch the shape of the tensor
bispectrum is enhanced in the squeezed limit, its amplitude can be amplified
with respect to slow-roll models, and tensor non-Gaussianity can exhibit a
scale dependence distinctive of our set-up. We prove that our results do not
depend on the frame used for the calculations. Squeezed tensor non-Gaussianity
induces a characteristic quadrupolar anisotropy on the power spectrum of the
stochastic background of primordial tensor perturbations. As a step to make
contact with gravitational wave experiments, we discuss the response function
of a ground based Michelson interferometer to a gravitational wave background
with such a feature.Comment: 34 pages, 4 figure
