B-Mode auto-bispectrum due to matter bounce

Primordial Gravitational waves leave polarization imprints on the Cosmic Microwave Background (CMB). In this article, we investigate polarization bispectrum, which is also referred to as the B-mode auto bispectrum, due to a matter bounce Universe. For simplicity, we consider a minimally coupled Einstein frame and obtain an analytical integral expression for the bispectrum and numerically perform the integration. We find that the signal-to-noise ratio is small, when compared with the same in the inflationary paradigm and hence quite difficult to detect in the future experiments. Thus a detection of tensor mode bispectrum in future will be helpful in ruling out matter bounce model. Also, to ease the numerical evaluation of the bispectrum, we develop and use various techniques. We believe that these techniques can be used in various other contexts.