Parity Violation of Gravitons in the CMB Bispectrum

We investigate the cosmic microwave background (CMB) bispectra of the intensity (temperature) and polarization modes induced by the graviton non-Gaussianities, which arise from the parity-conserving and parity-violating Weyl cubic terms with time-dependent coupling. By considering the time-dependent coupling, we find that even in the exact de Sitter space time, the parity violation still appears in the three-point function of the primordial gravitational waves and could become large. Through the estimation of the CMB bispectra, we demonstrate that the signals generated from the parity-conserving and parity-violating terms appear in completely different configurations of multipoles. For example, the parity-conserving non-Gaussianity induces the nonzero CMB temperature bispectrum in the configuration with Sigma(3)(n=1) l(n) = even and, while due to the parity-violating non-Gaussianity, the CMB temperature bispectrum also appears for Sigma(3)(n=1) l(n) = odd. This signal is just good evidence of the parity violation in the non-Gaussianity of primordial gravitational waves. We find that the shape of this non-Gaussianity is similar to the so-called equilateral one and the amplitudes of these spectra at large scale are roughly estimated as vertical bar b(lll)vertical bar similar to l(-4) x 3.2 x 10(-2) (GeV/Lambda)(2) (r/0.1)(4), where A is an energy scale that sets the magnitude of the Weyl cubic terms (higher derivative corrections) and r is a tensor-to-scalar ratio. Taking the limit for the nonlinearity parameter of the equilateral type as F-NL(eq) < 300, we can obtain a bound as Lambda greater than or similar to 3 x 10(6) GeV, assuming r = 0.1.