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We investigate the relation between the non-Gaussianities of the primordialperturbations and the sound speed of the tensor perturbations, that is, thepropagation speed of the gravitational waves. We find that the sound speed ofthe tensor perturbations is directly related not to the auto-bispectrum of thetensor perturbations but to the cross-bispectrum of the primordialperturbations, especially, the scalar-tensor-tensor bispectrum. This result isin sharp contrast with the case of the scalar (curvature) perturbations, wheretheir reduced sound speed enhances their auto-bispectrum. Our findings indicatethat the scalar-tensor-tensor bispectrum can be a powerful tool to probe thesound speed of the tensor perturbations.

Non-Gaussianities of primordial perturbations and tensor sound speed