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 $\sum_{n=1}^3 \ell_n = {\rm even}$ and, while due to the parity-violating non-Gaussianity, the CMB temperature bispectrum also appears for $\sum_{n=1}^3 \ell_n = {\rm odd}$. 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 $|b_{\ell \ell \ell}| \sim \ell^{-4} \times 3.2 \times 10^{-2} ({\rm GeV} / \Lambda)^2 (r / 0.1)^4$, where $\Lambda$ 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 $f_{\rm NL}^{\rm eq} < 300$, we can obtain a bound as $\Lambda \gtrsim 3 \times 10^6 {\rm GeV}$, assuming $r=0.1$.Comment: 23 pages, 3 figures. Accepted for publication in PTP. Version 3 includes errata in Fig.

CMB Bispectrum from Primordial Scalar, Vector and Tensor non-Gaussianities

We present an all-sky formalism for the Cosmic Microwave Background (CMB) bispectrum induced by the primordial non-Gaussianities not only in scalar but also in vector and tensor fluctuations. We find that the bispectrum can be formed in an explicitly rationally invariant way by taking into account the angular and polarization dependences of the vector and tensor modes. To demonstrate this and present how to use our formalism, we consider a specific example of the correlation between two scalars and a graviton as the source of non-Gaussianity. As a result, we show that the CMB reduced bispectrum of the intensity anisotropies is evaluated as a function of the multipole and the coupling constant between two scalars and a graviton denoted by $g_{tss}$; $|b_{\ell \ell \ell}| \sim \ell^{-4} \times 8 \times 10^{-18} |g_{tss}|$. By estimating the signal-to-noise ratio, we find that the constraint as $|g_{tss}| < 6$ will be expected from the PLANCK experiment.Comment: 19 pages, 4 figures. Accepted for publication in PT