Angular trispectrum of CMB temperature anisotropy from primordial non-Gaussianity with the full radiation transfer function

We calculate the cosmic microwave background (CMB) angular trispectrum, spherical harmonic transform of the four-point correlation function, from primordial non-Gaussianity in primordial curvature perturbations characterized by a constant nonlinear coupling parameter, fNL. We fully take into account the effect of the radiation transfer function, and thus provide the most accurate estimate of the signal-to-noise ratio of the angular trispectrum of CMB temperature anisotropy. We find that the predicted signal-to-noise ratio of the trispectrum summed up to a given l is approximately a power-law, (S/N)(<l)~2.2×10^-9fNL²l², up to the maximum multipole that we have reached in our numerical calculation, $l=1200$, assuming that the error is dominated by cosmic variance. Our results indicate that the signal-to-noise ratio of the temperature trispectrum exceeds that of the bispectrum at the critical multipole, lc~1500(50/|fNL|). Therefore, the trispectrum of the Planck data is more sensitive to primordial non-Gaussianity than the bispectrum for |fNL|50. We also report the predicted constraints on the amplitude of trispectrum, which may be useful for other non-Gaussian models such as curvaton models.