Parity violation in primordial tensor non-Gaussianities from matter bounce cosmology

It has been shown that primordial tensor non-Gaussianities from a cubic Weyl action with a non-dynamical coupling are suppressed by the so-called slow-roll parameter in a conventional framework of slow-roll inflation. In this paper, we consider matter bounce cosmology in which the background spacetime is no longer quasi-de Sitter, and hence one might expect that the matter bounce models could predict non-suppressed non-Gaussianities. Nevertheless, we first show that the corresponding non-Gaussian amplitudes from the cubic Weyl term with a non-dynamical coupling are much smaller than those from the conventional slow-roll inflation, in spite of the fact that there is no slow-roll suppression. We then introduce a dynamical coupling that can boost the magnitude of graviton cubic interactions and clarify that there is a parameter region where the tensor non-Gaussianities can be enhanced and can potentially be tested by cosmic microwave background experiments.