We investigate primordial non-Gaussianity in the inflation without an inflaton framework, where scalar perturbations are generated at second order by primordial gravitational waves in Einstein gravity on an exact de Sitter background. Since scalar modes are produced nonlinearly from tensor modes, non-Gaussianity is an intrinsic prediction of the mechanism. We compute the corresponding scalar bispectrum, derive the relevant contribution to the three-point function of the scalar potential, and evaluate its shape numerically. Similar to the scalar power spectrum, we find that the bispectrum depends on the number of observed e-folds $N_{\mathrm{obs}}$ through the ultraviolet cutoff. We show that the bispectrum shape is enhanced toward squeezed configurations, but its amplitude becomes strongly suppressed once the scalar power spectrum is normalized to the observed value. The resulting non-Gaussianity at cosmic microwave background scales is therefore negligibly small, well below present observational sensitivity.

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• Inflation
• Quantum cosmology