The tensor bi-spectrum in a matter bounce
  Matter bounces are bouncing scenarios wherein the universe contracts as in a
matter dominated phase at early times. Such scenarios are known to lead to a
scale invariant spectrum of tensor perturbations just as de Sitter inflation
does. In this work, we examine if the tensor bi-spectrum can discriminate
between the inflationary and the bouncing scenarios. Using the Maldacena
formalism, we analytically evaluate the tensor bi-spectrum in a matter bounce
for an arbitrary triangular configuration of the wavevectors. We show that,
over scales of cosmological interest, the non-Gaussianity parameter $h_{_{\rm
NL}}$ that characterizes the amplitude of the tensor bi-spectrum is quite small
when compared to the corresponding values in de Sitter inflation. During
inflation, the amplitude of the tensor perturbations freeze on super-Hubble
scales, a behavior that results in the so-called consistency condition relating
the tensor bi-spectrum and the power spectrum in the squeezed limit. In
contrast, in the bouncing scenarios, the amplitude of the tensor perturbations
grow strongly as one approaches the bounce, which suggests that the consistency
condition will not be valid in such situations. We explicitly show that the
consistency relation is indeed violated in the matter bounce. We discuss the
implications of the results.
